Bishop's first role was in Grange Hill. His second role, at age 16, was as Ben Quayle in Silent Witness. He played Stupid Brian in My Family; he appeared in three episodes. He starred in Muppet Treasure Island as Jim Hawkins. In 2002 he played Dick in the pantomime Dick Whittington.
In 2005 he portrayed the late comedian Dudley Moore onstage in Pete and Dud: Come Again, a drama charting Moore's turbulent relationship with Peter Cook, which debuted at the Assembly Rooms as part of the Edinburgh Fringe before transferring to The Venue in London's West End in March 2006. He appeared in Channel 4's satirical spoof documentary "Being Tom Cruise", from Star Stories on 2 August 2007 in which he played film star Tom Cruise. In September 2014 Bishop starred in "Fully Committed" at the Menier Chocolate factory. A one-man show with Bishop playing forty characters. Bishop's solo performance was well reviewed.