Bishop was born in San Diego, California, and attended Will C. Crawford High School. He had a major hit in 1977 with the song "On and On", which was a Number 11 hit in the U.S.; his other hits include "Save It for a Rainy Day", "Everybody Needs Love", "Something New in My Life" and "It Might Be You", the theme from the movie Tootsie. He has also performed many movie themes, including the theme from National Lampoon's Animal House which he sang in falsetto. Bishop's songs which have tracked on the Billboard Hot 100 chart are "It Might Be You". which peaked at Number 25 in 1983; "Save It For a Rainy Day" (#22, 1977); "On and On" (#11, 1977); and "Everybody Needs Love" (#32, 1978).

In addition to singing the theme song off-screen, Bishop had a cameo role in National Lampoon's Animal House as the aspiring folk singer whose guitar John Belushi smashes. Bishop still keeps the smashed guitar as a memento. He appeared in another John Landis movie, The Blues Brothers as the "charming trooper" who breaks his watch during the mall chase. Bishop also had a cameo in The Kentucky Fried Movie (1977), appearing as a hustler in the infamous "Catholic High School Girls in Trouble" segment. He was the musical guest on the March 11, 1978, episode of NBC's Saturday Night Live. Bishop also contributed the song The Heart Is So Willing for the 1986 remake of the film Mr. Blandings Builds His Dream House, called The Money Pit, starring Tom Hanks and Shelley Long. He also sung the end credit song, "We Can Do Anything", from Barney's Great Adventure. Patrick Bateman, the fictional anti-hero from Bret Easton Ellis' American Psycho, is an avowed fan of Bishop. He also provided soundtrack music for the Michael Douglas movie The China Syndrome.. Somewhere in Between.

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