Cooper was born in St. Petersburg, Florida. He played in a territory band with Nat Towles in Texas in the late 1940s, and gigged with Lionel Hampton in 1953. He played in the house band at the Apollo Theater in New York City in the mid-1950s, and following this spent time with Benny Goodman. Late in the 1950s he and his brother Steve formed a unit, the Cooper Brothers Band. From 1962 to 1969, he was a trombonist in Duke Ellington’s Orchestra. In 1973, he moved to Los Angeles and played in various jazz orchestras there over the next several decades; among them were The Juggernaut and Bill Berry’s L.A. band.
Cooper was the bandleader of the Buster Cooper Trio, at The Garden Restaurant, St. Petersburg, Florida.