Bishop spent nearly all of his film and TV career based in the UK, where he made his debut in a bit role in Stanley Kubrick's Lolita. Before long, he found himself in demand both as an on-screen and voice actor. His best-known work was for Gerry Anderson, for whom he provided the voice of Captain Blue in Captain Scarlet and the Mysterons. Most notably, he played Col. Ed Straker as star of Anderson's live-action UFO series. He also appeared in the original TV version of Whoops! Apocalypse and in a rare sojourn to the United States, provided voice acting work for the Star Trek: The Animated Series episode "The Magicks of Megas-Tu".
Bishop continued to act in film and TV until not long before his death in 2005.