The midfielder's second-half effort cancelled out Abdulai Bell-Baggie's first career league goal just before the half-hour for Tranmere, who failed to win at home for a fourth consecutive game.
The home side started the brighter, Michael O'Halloran running onto Jean-Louis Akpa Akpro's flicked header before shooting straight at County `keeper Bartosz Bialkowski.
Bell-Baggie then grabbed his first goal since notching against Chesterfield in the first round of the Capital One Cup, running on to O'Halloran's pass to shoot low past the onrushing Bialkowski.
But the Magpies - who saw a Julian Kelly shot saved by Owain Fon Williams in the first half - equalised after 74 minutes when Bishop rose highest to head in Alan Judge's free-kick.
Driven on by the goal, County substitute Jeff Hughes almost grabbed a winner shortly after but his shot from the right of the box bounced back of the left post.