Bingham's first professional appearance was in a production of Hair in his native Seattle. Bingham created the role of Caiaphas in the original concert tour of Jesus Christ Superstar and went on to perform the role in the original Broadway production, which ran from 1971–1973, as well as a Paris version. Along with Barry Dennen (Pilate) and Yvonne Elliman (Mary Magdalene), Bingham reprised his Broadway role in the 1973 film.
He retired from show business soon afterwards and worked in a managerial position in a zipper factory. He lives in Brewster, New York with his wife and two children.