Roland Bernard Berigan was born on November 2, 1908, in Hilbert, Wisconsin, the son of William Patrick Berigan and Mary Catherine (Mayme) Schlitzberg, and grew up in Fox Lake. He learned violin and trumpet and played in local bands as a teenager, including the University of Wisconsin's jazz ensemble, although he never attended the university. AllMusic adds that by age 12 he was playing in a youth band organized by his grandfather. Hal Kemp's orchestra turned him down at first, and he joined it in late 1929; his first recorded trumpet solos are with that band, which toured England and a few other European countries in 1930. Back in the United States late that year, he became one of New York's busiest studio trumpeters, working for Fred Rich, Freddy Martin, and Ben Selvin, and he joined the staff of the CBS radio network in early 1931. His first recorded vocal, "At Your Command," came with Rich that year. From late 1932 through early 1934 he sat in Paul Whiteman's orchestra, and he spent a short time with Abe Lyman's band in 1934. Between those jobs he freelanced on hundreds of commercial records, most notably with the Dorsey Brothers, led by Tommy Dorsey and Jimmy Dorsey, and with the Boswell Sisters. AllMusic's biography also places him in the pit band of the Broadway show Everybody's Welcome alongside the Dorsey brothers and Jack Teagarden, and in Rich's CBS studio band with Artie Shaw.

In 1935 he played on Glenn Miller's earliest recording as a leader, "Solo Hop," and joined Benny Goodman's new swing band. The producer John Hammond later wrote that he helped persuade Gene Krupa to rejoin Goodman by pointing out that Berigan, whom Krupa admired, had already signed on. With both of them in the lineup the band made the tour that reached the Palomar Ballroom in Los Angeles, where it opened on August 21, 1935, an engagement often credited with launching the swing era. Berigan took solos on Goodman records including "King Porter Stomp," "Sometimes I'm Happy," and "Blue Skies." He left Goodman to freelance again in New York, and from late 1935 through 1936 he began to record regularly under his own name. On December 13, 1935, he led a small group billed as Bunny Berigan and His Blue Boys for Decca, a session produced by Hammond for release in Britain on Parlophone, which yielded his compositions "Chicken and Waffles" and "Blues." He also backed singers such as Bing Crosby, Mildred Bailey, and Billie Holiday; session records list him on trumpet for two 1936 Holiday dates, July 10 and September 29. On April 13, 1936, he recorded "I Can't Get Started" for Vocalion, the first of two versions that made the song his theme. In the same years he was a regular on CBS Radio's Saturday Night Swing Club, appearing from 1936 into 1937.

He worked with Tommy Dorsey's orchestra in late 1936 and early 1937 as a jazz soloist on Dorsey's radio program and records, and his solo on the hit "Marie" became one of his signature performances; AllMusic also credits him with the trumpet solo on "Song of India." On March 31, 1937, he joined Dorsey, Fats Waller, guitarist Dick McDonough, and drummer George Wettling at Victor's New York studio for A Jam Session at Victor, an unrehearsed date built on "Honeysuckle Rose" and a blues; the record reached number four on the pop chart. Meanwhile he assembled a band of his own to record and tour, and on August 7, 1937, it recorded "I Can't Get Started" for Victor, with Berigan singing. Issued on Victor 25728 in 1938, it reached number 10 on the chart, and in 1975 it was inducted into the Grammy Hall of Fame. Over the next two years his orchestra made some of its best-known records for Victor, among them "Caravan" and "A Study in Brown" (August 18, 1937), "Livery Stable Blues" and "High Society" (September 13, 1938), and the late-1938 sides "Sobbin' Blues" and "Jelly-Roll Blues." Players in the band over the years included the drummers Buddy Rich, Dave Tough, George Wettling, Johnny Blowers, and Jack Sperling; the saxophonists Georgie Auld, Gus Bivona, Joe Dixon, Andy Fitzgerald, and Don Lodice; the pianists Joe Bushkin and Joe Lipman; the trombonist Sonny Lee; the bassists Hank Wayland and Morty Stulmaker; and the singers Danny Richards, Ruth Bradley, and Kathleen Lane.

Berigan led the band full-time from early 1937 until June 1942, apart from a six-month stretch in 1940 as a sideman with Dorsey. His alcoholism and a run of business misfortunes undermined the band's finances, and he declared bankruptcy in 1939. He had an affair with the singer Lee Wiley that lasted from 1936 into 1940. By September 1940 he was leading a small group, and he then put together another touring big band that did moderately well into early 1942. On April 20, 1942, he was hospitalized in Pittsburgh with pneumonia, and doctors found that cirrhosis had badly damaged his liver. They told him to stop drinking and stop playing; he did neither, rejoined the band on tour, and returned to his room at the Van Cortlandt Hotel in New York City, where he suffered a massive hemorrhage on May 31, 1942. He passed away two days later, on June 2, at Stuyvesant Polyclinic Hospital, at 33. He was buried in St. Mary's Cemetery south of Fox Lake, after a funeral at Saint Malachy's Roman Catholic Church in New York.

As he had wished, his band stayed together under his name, with his widow, Donna Berigan, holding his financial interest and tenor saxophonist Vido Musso taking over as leader. Victor issued a posthumous compilation of his band recordings in 1944. His 1937 "I Can't Get Started" has been used in films including Martin Scorsese's short The Big Shave (1967), Save the Tiger (1973), and Chinatown (1974). Fox Lake held an annual Bunny Berigan Jazz Jubilee from 1974 to 2018, and he was inducted into the ASCAP Jazz Wall of Fame in 2008. Two full-length biographies exist: Robert Dupuis's Bunny Berigan: Elusive Legend of Jazz (1993) and Michael P. Zirpolo's Mr. Trumpet: The Trials, Tribulations and Triumph of Bunny Berigan (2011).

Berigan modeled his trumpet style in part on Louis Armstrong's and often named Armstrong as his idol; Armstrong in turn praised his playing both before and after his death. AllMusic's Scott Yanow writes that from 1935 through 1939 he was regarded as the top trumpeter in jazz, with Roy Eldridge and Armstrong his main rivals, and describes a beautiful tone, a wide range with memorable low notes as well as upper-register shouts, and a willingness to take risks in a solo even when it occasionally failed. Most of his work was done inside dance orchestras and studio bands, which is why much of the evidence is in short 78 rpm solos: "Marie" and "Song of India" with Tommy Dorsey were so well known that Dorsey later had them written out and orchestrated for his whole trumpet section, according to AllMusic. His theme song outlived him. Wikipedia's list of recordings of "I Can't Get Started" includes versions by Billie Holiday with Lester Young (1938), Dizzy Gillespie (1945), Charlie Parker (1953), Sonny Rollins (1957), Ella Fitzgerald (1962), and Maynard Ferguson (1974), and Ferguson's profile describes his version as a tribute to Berigan.