Bishop was born on September 19, 1973 in Swindon, England. His father's career in the British Army prompted the family to move to Canberra, Australia when Bishop was six months old. He grew up in Australia, and earned his Performing Arts degree from Australia's National Institute of Dramatic Art in 1996, and he still serves as an acting tutor for students at his alma mater.
One of Bishop's first roles was in the Australian TV series Home and Away. Other TV credits include: McLeod's Daughters, Past Life, Necessary Roughness and The Glades. Bishop also starred alongside Dana Delany in the crime drama Body of Proof for the first two seasons of the series. In addition, he has a role in the upcoming film Stay Then Go slated for release this year.
Bishop currently lives with partner Claire Smith and their two children.