Bishop graduated from Australia's National Institute of Dramatic Art (NIDA) with a degree in Performing Arts (Acting) in 1996, and has been a regular screen acting tutor there since 1997. He was a 2006 Australia Day Ambassador.

Bishop is most recognized by his role for three seasons as Detective Peter Baker in the Australian series Home and Away. In 2002, Bishop appeared in the critically acclaimed film Walking on Water. Additional television credits include Fox Past Life, Hustle, McLeod’s Daughters, Heartbreak High, Water Rats, Blue Heelers, Farscape, White Collar Blue and All Saints. He also starred in the movies The Sugar Factory (1998), Occasional Coarse Language (1998), My Mother Frank (2000), Punishment and The Land of the Astronauts (2010). In 2011, he guest starred in an episode of the USA Network series Necessary Roughness entitled "Anchor Management".

Bishop currently resides in West Hollywood. He has two children with Claire Smith, Ava (born 2006) and Harrison (born 2009).

Bishop co-starred in the first two seasons of Dana Delany's medical drama television series Body of Proof in which he played medico-legal investigator Peter Dunlop, assistant to Medical Examiner Dr. Megan Hunt. In May 2011, it was announced that Body of Proof was renewed for a second season for the fall of 2011. He was written out of the show after two seasons. In June 2014 Bishop played Ryan McQuaid, a former Navy SEAL turned private contractor Billionaire in Season 5 of Covert Affairs.