Bishop was born in Bromley on 18th June 1980. After appearing on the television series, Grange Hill, he was cast as Jim Hawkins in Muppet Treasure Island (1996). He subsequently appeared in several British television series, including Pie in the Sky (1994), Love Soup (2005), My Family (2000), Peep Show (2003), and Spoons (2005). He also played the title role in the 2002 television film Dick Whittington (2002), as well as the lead role in the 2002 film Food of Love (2002). He also appeared in the film Suzie Gold (2004), which also starred Summer Phoenix.

In 2005, he played comedian Dudley Moore on stage in "Pete and Dud: Come Again," a drama that charted Moore's turbulent relationship with Peter Cook, which debuted at the Assembly Rooms as part of the Edinburgh Fringe before transferring to he Venue in London's West End in March 2006.

He was also seen in the Channel 4 British Comedy Awards 2006 award-winning comedy Star Stories (2006).

He is now appearing in the UK adverts for the bank NatWest, and his own pilot sketch show "Comedy Showcase--Kevin Bishop" for channel 4, which was also commissioned as six-part series for fall 2007.