He began his career playing alto saxophone at ten for the school band and by 12 was playing at Luso-American dances. In 1966 he was in Bobby Freeman's band and after this he began his associations with well-known groups.
His role in these bands was primarily as a saxophonist. His most notable was with the Doobie Brothers and Steely Dan. In 2002 he worked on the Big Blue Earth project sponsored by the Church of Christ, Scientist. Bumpus enjoyed a short tenure with Café Society, a Los Angelespopband, during the 1980s where he played in a horn section with the trombonist Dan Levine and trumpeter Anne Petereit King. In 1981, Bumpus issued his first solo LP, A Clear View, which featured his singing, writing and sax playing, stretching out with the band on several, long, jazzy jams over 6 minutes each. Bumpus died of a heart attack in 2004 while on a flight from New York to Los Angeles, aged 58.