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. In August 2007 he appeared as the title character in Channel 4's satirical spoof documentary "Being Tom Cruise", a spin-off of Star Stories. In September 2014, Bishop appeared in the one-man show Fully Committed at the Menier Chocolate Factory, in which he played forty characters.
In 2016 Bishop played Nigel Farage in a one-off BBC2 comedy entitled Nigel Farage Gets His Life Back.
In 2017, Bishop became the speaking voice for 2D, fictional lead singer of British virtual band Gorillaz.