The striker had levelled with a coolly taken penalty after 56 minutes, but his training ground free-kick late on was the icing on the cake.
New boss Alan Knill was happy to be playing on his lucky ground and his side made the most of it by bagging their first league win since November 17.
Bradford skipper David Wetherall had a luck escape early on when his defensive header bounced away of a post, but the Bantams looked full value for their early lead.
In-form striker Peter Thorne made the breakthrough with his fifth goal in six games, but the home side couldn't build on their advantage.
Bury's backline was caught ball watching after 22 minutes when midfielder Tom Penford fired over a cross and Thorne showed his quality with a neat flick header which flew beyond the reach of on-loan keeper Darren Randolph.
Lee Bullock came close to adding a second for City just before the break but Randolph bravely blocked his close-range volley.
A City break was harshly halted by an offside flag as full-back Ben Starosta surged towards the Bury box, but Bury came out fired up after the interval.
Centre-half Dave Challinor had tested City with his long throws and it was another of his bombs which led to Wetherall hauling down giant defender Ben Futcher in the box.
Bishop calmly sent City keeper Scott Loach the wrong way with his spot-kick and Knill's men scented a much-needed victory.
Loach kept City in the game with stunning saves to deny winger Elliott Bennett and Nicky Adams, but he could do nothing about Bishop's sensational winner.
Wetherall was penalised for a foul on Adam Rooney and, as City lines-up expecting a direct shot, the ball was rolled to Bishop who took the pass in his stride before unleashing a fierce right-foot shot from 20 yards out.