An original member of Herb Alpert's Tijuana Brass, Bob worked and recorded with artists such as Harry James, Benny Goodman, Dizzy Gillespie, Shelly Manne, Terry Gibbs, Gerald Wilson and others from 1953-1983. He also worked extensively as a studio musician on numerous scoring sessions for film and television productions. As a young musician Edmondson began his career on trombone in Phil Moore's marching band, playing in off shoot ensembles such as his German band and dance band. Well it was the 50's.
In 1952 Edmondson and Herb Alpert met as high school musicians. In 1962, following the release of the single of The Lonely Bull, Alpert and his partner Jerry Moss formed a record label, using the initials of their last names. A&M Records was born. Bob initially worked with the TJB when they appeared in public for the first time at The Crescendo in Los Angeles in 1963. He then recorded with The Tijuana Brass on South of the Border and on all subsequent albums and helped organize what became the performing group.