Bradley was known for loving all kinds of music, but he was especially a jazz music enthusiast. He hosted the Peabody Award–winning "Jazz at Lincoln Center" on National Public Radio for over a decade until just before his death. A big fan of the Neville Brothers, Bradley performed on stage with the bunch, and was known as "the fifth Neville brother". Bradley was also friends with Jimmy Buffett, and would often perform onstage with him, under the name "Teddy". Bradley had limited musical ability and did not have an extensive repertoire, but would usually draw smiles by singing the 1951 classic by Billy Ward and the Dominoes, "Sixty Minute Man".