Bobby Durham was born in Philadelphia and learned to play drums while a child. He played with The Orioles at age 16, and was in a military band between 1956 and 1959. After his discharge he played with King James and Stan Hunter. In 1960 he moved to New York City, where he played with Lloyd Price, Wild Bill Davis, Lionel Hampton, Count Basie, Slide Hampton, Grant Green, Sweets Edison, Tommy Flanagan, Jimmy Rowles, and the Duke Ellington Orchestra, in which he played for only five months. While working with Basie he met Al Grey, and was a member of several of Grey's small ensembles. He accompanied Ella Fitzgerald for more than a decade, and worked with Oscar Peterson in a trio setting.
Durham also played in trios with organists such as Charles Earland and Shirley Scott, and there was a resurgence in interest in Durham's work during the acid jazz upswing in the 1990s. Many of Durham's projects, both as sideman and as leader, have come due to his association with producer Norman Granz, who had him work with Ella Fitzgerald, Count Basie, Harry Edison, Flanagan, and Joe Pass. Durham has led his own combos as well; he is noted for scat singing along with his drum solos. Durham has also performed often with pop and soul musicians such as Frank Sinatra, James Brown, Ray Charles, and Marvin Gaye.