Robert "Bobby" Shew was born March 4, 1941, in Albuquerque, New Mexico. He started on guitar at eight before switching to trumpet at ten, and was largely self-taught on the instrument from there. Drafted into the U.S. Army in 1960, he spent his service years, 1960 to 1963, playing in the NORAD Joint Forces Band in Colorado Springs, Colorado, a posting that kept him playing full-time through his early twenties.

After his discharge, Shew worked the touring ghost band circuit, joining a Tommy Dorsey orchestra before moving into two of the era's most demanding lead-trumpet chairs: Woody Herman's orchestra, where he can be heard on the 1966 album Woody's Winners, and then Buddy Rich's newly re-formed big band, documented on 1966's Swingin' New Big Band and 1967's Big Swing Face. The Rich and Herman years built his reputation as one of the era's most reliable high-note lead players rather than as a jazz soloist in his own right.

That reputation carried him to Las Vegas, where he settled into the hotel and show-band circuit, working as featured trumpeter in Tom Jones's backing band and appearing on Jones's 1971 live album Live at Caesar's Palace. Steady, well-paid Vegas work was exactly the kind of career many lead trumpeters never left, but late in 1972 Shew relocated to Los Angeles specifically to develop as an improviser rather than stay a section specialist.

The move paid off immediately. Shew became one of the busiest trumpet players on the Los Angeles studio scene, turning up on sessions for Barbra Streisand's A Star Is Born soundtrack, Herbie Hancock's Sunlight (1978), and dates for Neil Diamond, Donna Summer, Vikki Carr, and the Beach Boys, while simultaneously working the brass sections of the city's top working big bands through the rest of the decade: Louie Bellson's orchestra, Maynard Ferguson's band, and, most enduringly, the Toshiko Akiyoshi-Lew Tabackin Big Band. Shew is credited on the Akiyoshi-Tabackin band's entire run of celebrated RCA and Baystate-era studio and live albums, from Kogun (1974) through Long Yellow Road (1975), Insights, Tales of a Courtesan (Oirantan), and Road Time (all 1976), March of the Tadpoles and Live at Newport '77 (1977), and Salted Gingko Nuts, Sumi-E (1979), and Live at Newport II (1980), sharing the brass and reed sections with a rotating cast of fellow West Coast studio players including baritone saxophonist Bill Perkins and alto saxophonists Gary Foster and Dick Spencer.

Shew's own run as a leader took off at the same time. Class Reunion (1980, Sutra) and Outstanding in His Field (1980, Inner City, a 1980 Grammy nominee) established him as a small-group leader, followed in quick succession by Play Song (1981, his sextet), Debut (1981, a quartet date cut for the Japanese Discomate label), and You and the Night and the Music (1981, credited to Bobby Shew & His West Coast Friends, with alto saxophonist Bud Shank in the front line). The same period produced two European duo dates, Telepathy with pianist Bill Mays and Dialogic with Swedish trumpeter Jan Allan, plus the twin-trumpet summit Trumpets No End (1984) with fellow studio veteran Chuck Findley, the quartet album Breakfast Wine (1985, with a young Makoto Ozone on piano), and the sextet date Shewhorn (1986).

He kept recording steadily into the 1990s and 2000s: Tribute to the Masters (1995, with Jamey Aebersold), Heavyweights (1996, co-billed with trombonist Carl Fontana), Playing With Fire (1997, a 1986 session paired with fellow trumpeter Tom Harrell), the Latin-jazz date Salsa Caliente (1998), Play the Music of Reed Kotler (2001, a second documented duo billing with Gary Foster), and Live in Switzerland (2002, co-led with Swiss saxophonist George Robert). Alongside the recording career, Shew built a parallel reputation as one of jazz education's most in-demand trumpet clinicians, teaching internationally in Austria, Germany, the Netherlands, Switzerland, and Canada (including a 2017 residency at Austria's Graz University of Music), leading workshops at the Skidmore Summer Jazz Institute in Saratoga Springs, New York, directing the Albuquerque Jazz Orchestra, and lending his name to a Yamaha signature trumpet model, the YTR-8310Z. As of 2026 Shew is 85 and still active as a performer and clinician.

Shew is unusual among his generation of big-band lead players for combining two skills that rarely coexist in one trumpeter: the stamina and upper-register command to anchor a lead chair through an entire Buddy Rich or Toshiko Akiyoshi chart, and the harmonic fluency and warm flugelhorn tone to front his own small-group dates as an improviser. Largely self-taught, he became known in later decades less for any single stylistic signature than for versatility across settings, from the West Coast cool-toned quartet and quintet sessions that make up most of his own catalog to the Latin-jazz turn of Salsa Caliente and the big-band session work that defined his 1960s and 1970s reputation. That range, combined with decades of clinics and workshops worldwide, made him one of the most widely cited trumpet educators of his generation, with a teaching emphasis, by his own and his students' accounts, on musicality, breath efficiency, and taste over raw technique.