From 1946 to 1948 he studied clarinet and soprano saxophone with Sidney Bechet. From 1948 to 1950 he led his own combo in Boston and in 1951 played with Sid Catlett and De Paris brothers. In 1952 he turned to modern jazz, studied with Lennie Tristano and attended the Manhattan School of Music.

From 1954 to 1956 he played primarily West Coast Jazz with his group "The Six". Subsequently he again turned to Dixieland and played with Eddie Condon, Max Kaminsky, Benny Goodman, Bob Hackett a. o. He also worked with the Yank Lawson & Bob Haggart band. For some time he has led the group Bechet Legacy, with which he perfomed at the IJFB in 1984.

Bob Wilber was musical director for Francis Ford Coppola's film "Cotton Club".