Bob Stewart was born in Sioux Falls, South Dakota, on February 3, 1945, while his father, Riley Stewart, was stationed at the Army Air Force base there. Riley Stewart had been a pitcher in the Negro Leagues, with the Chicago American Giants and the New York Cubans. When the base closed the family moved east, to New York and then to Newport, Rhode Island, in 1953, where Stewart spent part of his childhood with his grandparents and first heard jazz. He picked up the trumpet around 1955, at about ten years old, and the family moved again to Philadelphia in 1960. At West Philadelphia High School he studied under Wendell Pritchett, and he went on to the Philadelphia College of the Performing Arts, a conservatory so hostile to the music that jazz was not permitted in the practice rooms. Stewart remembers a student trio playing a jazz piece at a performance hour and the head of the school setting off the fire alarm from the back of the room.

The switch to tuba was forced on him. Embouchure trouble ended his trumpet playing at the close of his second year, and rather than lose a year he moved to the low brass, trained new muscles, and took his graduation recital on the tuba. He later described it as a blessing in disguise. His first steady work came in 1967 in Dixieland bands at Your Father's Mustache and the Red Garter, then close to the only rooms in which a tuba player could get hired, and it was at the Red Garter that he met Howard Johnson. Through that winter and the following spring he taught public school in Philadelphia and drove to New York at weekends to work the club, sit in with Johnson's tuba ensemble Substructure, which later became Gravity, and hang around Slugs'. In June 1968 he moved to New York for good. Carla Bley was assembling the Jazz Composer's Orchestra and hired him or Johnson as the chair required, and when Johnson could not make a date with Gil Evans, Stewart subbed. Those were his first jobs in contemporary jazz.

His earliest recordings put him at the centre of a specific experiment: the tuba section that Howard Johnson wrote for Taj Mahal. On The Real Thing (Columbia, 1971), cut live at the Fillmore East, Johnson's brass arrangements are scored for four low brass players. Johnson took double B-flat and F tuba plus flugelhorn and baritone saxophone, Joe Daley took double B-flat tuba and valve trombone, Earl McIntyre took E-flat tuba and bass trombone, and Stewart is credited on double-C tuba, flugelhorn and trumpet, the only session on which his first instrument shows up next to his second. The same year he sang in the chorus of Carla Bley and Paul Haines's Escalator Over the Hill on JCOA, a credit for voice rather than tuba, and played in the Brass Company, a brass group led by Bill Lee that also carried Billy Higgins and Clifford Jordan and issued Colors on Strata-East.

Charles Mingus came next, and again through Howard Johnson. Stewart was subbing on the tuba chair, Mingus liked both players, and turned it into a double chair: Johnson on baritone saxophone and Stewart on tuba, or the two of them the other way around. The studio result was Let My Children Hear Music (Columbia, 1972). The live one was the concert of February 4, 1972 at Philharmonic Hall, issued the following year as Charles Mingus and Friends in Concert, where Stewart's tuba sits in a horn section that also holds Gerry Mulligan, Lee Konitz, James Moody, Gene Ammons, Charles McPherson, Jon Faddis and Milt Hinton, with Dizzy Gillespie singing. "I didn't know it at the time," Stewart said later, "but I was a part of a certain kind of history."

The question that shaped the rest of his career was asked in 1976. Stewart and the alto saxophonist Arthur Blythe were both playing in Gil Evans's orchestra, and Blythe asked him whether he could play bass on the tuba. Stewart said yes and then spent a year working out how. The problem was not which notes to choose. A bassist does not have to breathe to make a sound, and a tuba player does, so Stewart had to build a breathing technique that would not disturb the pulse, along with the endurance to hold a bass chair for a whole evening and a harmonic vocabulary the instrument did not have. Nobody could tell him which microphone to use or where to put it on the horn. Blythe wrote his own material, so there were no other bassists' versions to study. The results are on record from February 26, 1977, when a single night at the Brook on West 17th Street produced both The Grip and Metamorphosis for India Navigation, and on Bush Baby (Adelphi, 1978), a trio of alto saxophone, tuba and congas with no other instrument at all. Lenox Avenue Breakdown (Columbia, 1979), with Cecil McBee, Jack DeJohnette, James Newton and James Blood Ulmer, carries the solo that made his reputation; the editors of The Penguin Guide to Jazz called it "one of the few genuinely important tuba statements in jazz." The partnership ran more than thirty years, through Illusions, Blythe Spirit, Elaborations, Light Blue, Da-Da, Hipmotism, Night Song and the three Savant records of 2000 to 2003, and ended with Exalted Conversation, a duo concert recorded in 2003 at St. Paul's Chapel, Columbia University, presented by the Center for Jazz Studies under Robert O'Meally.

Two other long associations ran alongside it. Stewart held the tuba chair in Gil Evans's orchestra from the mid-1970s, on There Comes a Time (RCA, 1976), the live Priestess recorded at St. George's Church in May 1977, Little Wing from Germany in 1978, the Royal Festival Hall concerts of 1978 and the Tokyo dates of 1976, and he worked in the Carla Bley Band on Dinner Music, European Tour 1977, Musique Mecanique and Fleur Carnivore. In 1984 Lester Bowie put together Brass Fantasy, a band of brass and drums with no bass and no chordal instrument, and Stewart was in it from the first tour to Bowie's death: I Only Have Eyes for You was recorded in February 1985 at Rawlston Recording in Brooklyn and issued by ECM, and Avant Pop, Twilight Dreams, My Way, The Fire This Time and The Odyssey of Funk and Popular Music followed. He also recorded with McCoy Tyner on Song of the New World and 13th House, with Dizzy Gillespie and Machito on Afro-Cuban Jazz Moods for Pablo, with the Globe Unity Orchestra, with Muhal Richard Abrams, with David Murray's big band at Sweet Basil, and with Sonny Rollins, Don Cherry, Sam Rivers, Uri Caine and Howard Johnson's all-tuba Gravity. The pop credits are real and specific rather than decorative: two tracks of Chaka Khan's Naughty in 1980, one track of David Byrne and St. Vincent's Love This Giant in 2012.

His own catalogue is small and deliberate. First Line was cut at RPM Sound Studios in November 1987 and mixed the following January, a band of tuba, trumpet, trombone, guitar and drums with no bass, and Goin' Home followed from the same room in December 1988 under the name Bob Stewart's First Line Band, with Steve Turre, James Zollar, Jerome Harris and Buddy Williams, guest appearances by Ed Blackwell, Earl Gardner, John Clark and Frank Colon, and tunes by Kelvyn Bell, Don Cherry, Olu Dara and Billy Harper alongside his own. Then and Now (Postcards, 1996) drew on sessions from October 1995 and March 1996 and brought in Taj Mahal on two tracks and Carlos Ward with Graham Haynes on four. A duo record with the trombonist Ray Anderson, Heavy Metal Duo: Work Songs and Other Spirituals, came out in 2004, and Rainbow Country, co-led with the Belgian percussionist Chris Joris, was recorded in May 2006. A live duo with the pianist Dave Burrell, taped at the Kölner Stadtgarten on June 13, 1994, sat unreleased for twenty-two years until NoBusiness issued it as The Crave on LP in 2016 in an edition of four hundred.

Connections: Mind the Gap (Sunnyside, August 5, 2014) is the fullest statement of the idea. Stewart called the band the Double Quartet: the First Line Band, with Jerome Harris on guitar and Matt Wilson on drums, joined by the strings of PUBLIQuartet, whose violinist is his son Curtis Stewart. He commissioned a five-part suite, In Color, from the violinist and composer Jessie Montgomery, built on multiphonic techniques of his own, then broke the suite apart and interleaved its movements with arrangements of pieces by the people who had hired him: Arthur Blythe's "Bush Baby" and "Odessa," Frank Foster's "Simone," Thelonious Monk's "Monk's Mood," Mingus's "Jump Monk," Piazzolla's "Libertango" and Harris's "Hand by Hand," with Nick Finzer on trombone and Randall Haywood on trumpet added for the last two.

Teaching has run in parallel with all of it and was never a fallback. Stewart taught in Pennsylvania public schools, then at Fiorello H. LaGuardia High School in New York, where the jazz ensemble he directed won the Essentially Ellington national competition. He took a bachelor's degree in music education from the Philadelphia College of the Performing Arts and a master's in education from Lehman College, where he is a distinguished lecturer, and he has been on the faculty of the Juilliard School since 2001 as a professor of jazz history. He works with Jazz at Lincoln Center as an educational consultant and an adviser to its Rhythm Road project, helped write the curriculum for its Middle School Jazz Academy, has served on a New York State Council on the Arts panel, consulted for JazzMobile and taught at the Louis Armstrong Summer Jazz Camp in New Orleans. He has run brass clinics in Austria built around the Brass Fantasy repertoire, and in 2012 he founded the Annual Bob Stewart Tuba Competition, whose stated purpose is to push tuba players to lead their own ensembles and build a repertoire for the instrument. He appears in Ken Burns's Jazz and is the subject of the feature documentary Jazz on a Winter's Day. He has kept recording: Michael Blake's Combobulate (Newvelle, 2022) is a brass sextet with two tuba players, Stewart and Marcus Rojas, and Alex Harding and Lucian Ban's Blutopia (Sunnyside, 2024) features him by name.

Stewart's contribution is easy to state and was hard to make: he took an instrument that had been retired from jazz in the 1930s and put it back in the rhythm section as the bass, not as a novelty and not as a front-line horn. Howard Johnson had already shown what a tuba could do as a melody instrument, playing high and fast in a way Stewart flatly says nobody else could match, so Stewart went the other way and worked the bottom of the horn. What that required was a set of solutions with no precedent: circular and staggered breathing that keeps a walking line from lurching every four bars, an embouchure that survives three hours of it, amplification and microphone placement worked out from scratch, and a harmonic approach that lets a single-line instrument imply changes the way a bass does. The models he reached for were not tuba players. He has said the singer Johnny Hartman has the same range as the tuba and taught him how to shape a melody and how to write brass parts that leave the tuba room; and that his time feel and his comping come from left hands, from the organist Big John Patton and from Thelonious Monk, whose stride-derived two-beat pattern under his own right-hand figures Stewart identified with directly.

The playing is warm, breathy and physical, with a big attack and a soloist's line rather than a section player's, and it does its most characteristic work in bands built with a hole where the bass usually goes. That is not a coincidence: Blythe's Bush Baby is a trio of alto, tuba and congas, Brass Fantasy is brass and drums, and both of Stewart's own First Line records leave the bass chair empty and hand the job to him. The influence has been wide and is acknowledged by name. Writing after Arthur Blythe's death, Stewart pointed out that the question Blythe asked him in 1976 has since been put to at least three generations of tuba players, and that Henry Threadgill, Carla Bley, Steven Bernstein and Charlie Haden all went on to build tubas into their ensembles. Reviewers have treated the Lenox Avenue Breakdown title-track solo as the single document that settled the argument.