Bodner played with Benny Goodman in the 1950s, including on the soundtrack of The Benny Goodman Story (1955); since Goodman was his own principal clarinetist, Bodner played alto sax. He worked most often as a session musician, particularly with Miles Davis, and also accompanied Billie Holliday, Frank Sinatra, Tito Puente, George Benson, The Bee Gees (on Mr. Natural), Carly Simon, Grace Slick, Billy Taylor, and Bette Midler, and with fellow Sesame musicians Toots Thielemans (Contrasts) and Mel Davis (Music for Weight Watchers).