After leaving college in 1960, Shew was drafted into the U.S. Army and played trumpet with the NORAD band in Colorado Springs and on tour. After leaving the Army, Shew joined Tommy Dorsey's band and then played with the Woody Herman and then the Buddy Rich big bands in the mid- to late 1960s. In 1972 Shew moved from Las Vegas to Los Angeles where he did much studio work as well as play with some of the top big bands of the era through the end of the 1970s: Akiyoshi/Tabackin, Bellson, Ferguson, and others. In addition to playing on several notable big band recordings starting in the 1960s, Shew recorded several albums as leader, starting with Telepathy in 1978.
Shew has mentored jazz musicians in New Mexico, and has led the Albuquerque Jazz Orchestra. He has taught a two-week workshop for high school students at the Skidmore Summer Jazz Institute in Saratoga Springs, New York, Shew also performs and teaches worldwide, including a two-week residency at the Graz University of Music in Austria in 2017. He has taught at leading European music schools in Austria, Germany, the Netherlands, and Switzerland, and also in Canada.
- Telepathy (Jazz Hounds) 1978
- Outstanding In His Field (Inner City) 1979
- Class Reunion (Sutra) 1980
- Play Song (Jazz Hounds) 1981
- Shewhorn (Pausa) 1983
- Trumpets No End (Delos) 1983 – with Chuck Findley
- Breakfast Wine (Pausa) 1984
- Round Midnight (MoPro) 1984
- Aim For The Heart (Gateway) 1987 – with the Wigan Youth Jazz Orchestra
- Metropole Orchestra (Mons) 1988
- Tribute to the Masters (Double-Time Records) 1995
- Heavyweights (MAMA) 1996 – with Carl Fontana
- Playing With Fire (MAMA) 1997
- Salsa Caliente (MAMA) 1998
- The Music of John Harmon (Sea Breeze) 2001
- Play Music of Reed Kottler (Torii) 2002 – with Gary Foster "and friends"
- Live in Switzerland (TCB) 2003 – Bobby Shew / George Robert Quintet
- I Can't Say No (Four Leaf Clover) 2003
- One in a Million (Sea Breeze) 2004 – recorded 1990 with The Groovin' High Big Band / Peter Fleischhauer
- Cancaos Do Amor (Torii) 2007
- LIVE 1983 (UF School of Music) 2015 -Recorded 1983 with University of Florida Jazz Band -Director Gary Langford
With Louis Bellson
- The Louis Bellson Explosion (Pablo, 1975)
With Carmen McRae
- Can't Hide Love (Blue Note, 1976)
With Rodger Fox Big Band
- Heavy Company (Circular, 1981)
With Gerald Wilson
- State Street Sweet (MAMA, 1995)
- Outstanding in His Field - Grammy nomination (1980)
- Bobby Shew, trumpet – New Mexico Philharmonic Retrieved 2018-08-31.
- Bobby Shew interview at JazzWaxx.com
- Bobby Shew biography at JazzTrumpetSolos.com Archived July 20, 2011, at the Wayback Machine
- Dix, John (April 2, 2016). "Rodger Fox Profile". audioculture.co.nz.
- 1980 Grammy awards database at metrolyrics.com