Clifford Everett Shank Jr. was born on May 27, 1926, in Dayton, Ohio, and was raised on a farm. He started on clarinet around age ten and moved to saxophone a couple of years later. He studied music at the University of North Carolina from 1944 to 1946 but left in his third year to go on the road with a band that folded after a few weeks, and instead of going back to school he went to California. While sharing rooms with other young musicians in Los Angeles he picked up the flute through a roommate's teacher, studied with the trumpeter and arranger Shorty Rogers, and worked in the big bands of Charlie Barnet and Alvino Rey. At the end of the 1940s he joined Stan Kenton's orchestra, and as lead alto and flute in its Innovations in Modern Music Orchestra he became one of the band's featured young players; he left Kenton in 1951.

As a freelancer he was soon at the center of the Los Angeles scene. He worked with Rogers's small groups and with the tenor saxophonist and oboist Bob Cooper, and in 1952 he joined bassist Howard Rumsey's Lighthouse All-Stars, the house band at the Lighthouse Cafe in Hermosa Beach. His flute and Cooper's oboe made an unusual front line. In 1953 and 1954 he recorded for Pacific Jazz with the Brazilian guitarist Laurindo Almeida, several years before the bossa nova craze reached the United States; the quartet's album, later reissued as Brazilliance, made his name beyond Los Angeles. DownBeat named him New Star Alto in its critics' poll, and Metronome picked him as its Arrival of the Year for 1954. For the same label he made albums with Rogers and Bill Perkins, with the trombonist Bob Brookmeyer, and with Cooper. He left the All-Stars in 1956 to lead his own quartet with the pianist Claude Williamson, bassist Don Prell and drummer Chuck Flores, and that year he topped DownBeat's readers' poll as best flutist, beating Herbie Mann in the poll's new flute category. In 1958 he was among the first American jazz musicians to record in Italy, making string-backed ballad albums in Milan with the conductor Ezio Leoni, who worked as Len Mercer.

During the late 1950s and the 1960s he made a long run of albums for World Pacific and Pacific Jazz that took in surf-film music, Japanese koto, Indian classical music and Brazilian jazz. He wrote and played the music for Bruce Brown's surf films Slippery When Wet and Barefoot Adventure, recorded Koto & Flute (1960) with the koto player Kimio Eto, and in 1962 played flute on Ravi Shankar's Improvisations. He made two bossa nova albums with the pianist Clare Fischer, Bossa Nova Jazz Samba (1962) and Brasamba! (1963, with the guitarist Joe Pass). As club and recording work for jazz players thinned out, he became a first-call studio musician in Hollywood, playing on film, television and pop sessions, among them the alto flute solo on the Mamas & the Papas' "California Dreamin'" (1965) and a solo on the Association's "Windy." He still made his own records: Michelle (1966), with Chet Baker on flugelhorn and arrangements by Bob Florence, reached number 56 on the chart, and Windmills of Your Mind (1969) set the music of Michel Legrand, who also arranged it, for alto and flute.

In 1974 he formed the L.A. Four with Almeida, bassist Ray Brown and drummer Shelly Manne, who was replaced by Jeff Hamilton after 1977; the group toured Australia in 1975 and made ten albums, mostly for Concord Jazz, before disbanding in 1982. Through the 1970s and 1980s he recorded for Concord, Muse and Contemporary, and by the late 1980s he had stopped playing flute to concentrate on the alto saxophone. In the 1990s he made albums for Candid, Fresh Sound and Milestone, reunited with former Lighthouse All-Stars for a 40th anniversary concert in 1989 and for further recordings in 1991 and 1992, and for 21 years, until 2004, directed Jazz Port Townsend, the summer jazz workshop at the Centrum arts center in Port Townsend, Washington.

In 2005 he formed the Bud Shank Big Band in Los Angeles, and the next year it recorded Taking the Long Way Home for Jazzed Media. He also made a duo album with the pianist Bill Mays, Beyond the Red Door (2007), and in July 2006 recorded an episode of NPR's Piano Jazz with Marian McPartland. In 2008 the Tucson Jazz Society and the Los Angeles Jazz Society each gave him a lifetime achievement award, and a documentary, Bud Shank: Against the Tide (Portrait of a Jazz Legend), directed by Graham Carter, came out from Jazzed Media. He had moved to Tucson, Arizona, for health reasons. On April 2, 2009, he passed away at his home there of a pulmonary embolism, a day after returning from a recording session in San Diego. He was 82.

Shank began his career labeled a West Coast cool-school player, but AllMusic's Chris Kelsey argues that listeners who followed him over the long run heard one of the hottest and most original altoists of the generation after Charlie Parker, and that in his later years he had more in common with Jackie McLean or Phil Woods than with Paul Desmond or Lee Konitz. His alto sound was keening, melodic and expressive. Marian McPartland, hosting him on Piano Jazz, called him beyond compare, and NPR's write-up of that session described him as a straight-ahead bebop player more than a cool stylist. On flute, which he played until the late 1980s, he was among the first modern jazz players to record with the instrument. Much of his best-known work reached outside the usual jazz repertoire: Brazilian music with Almeida and Clare Fischer, Indian and Japanese collaborations with Ravi Shankar and Kimio Eto, surf-film scores, and the chamber-flavored, Latin-tinged small-group jazz of the L.A. Four, which he helped popularize. Alongside all this he kept up a busy second career in the Hollywood studios.