Bates is the brother of Bob Bates. He played in Jimmy Dorsey's band in 1945-46 and with Raymond Scott and Carmen Cavallaro shortly thereafter. In 1948 he played in a trio with Dave Brubeck, and in 1949 with Paul Desmond. He recorded with Jack Sheedy's Dixieland Jazz Band in 1950. After spending four years in the Air Force, Bates played with Wally Rose's Dixieland Band in 1955 and then replaced his brother in Brubeck's quartet, playing on the album Jazz Goes to Junior College among others. He also recorded with Desmond's group again in 1956. In 1957 he left Brubeck, and led a trio in San Francisco.