Just one goal in five games had contributed to a wretched run of five straight home defeats, but the Shakers returned to winning ways with a comfortable victory at Gigg Lane.
Bishop gave the Shakers a ninth minute lead before Hurst scored his first goal of the season in the 40th minute.
They both struck inside five minutes around the hour-mark to seal the three points and avenge their FA Cup defeat by Gillingham two weeks ago.
Bury made a lively start and were rewarded with a ninth minute opener when Mike Jones' teasing left-wing cross cut open the Gillingham defence and Bishop pounced to stab the ball home from close range.
Gillingham replied with Adam Miller flashing a shot across goal and a timely challenge by Shakers skipper Paul Scott denied Mark Bentley a shot at goal.
Hurst then got to the byline for Bury and his cut-back was steered narrowly over by Bishop, while a Garry Richards header tested Bury keeper Wayne Brown from John Nutter's 29th minute corner.
Visiting keeper Simon Royce made a fine save to deny Hurst after a Bury corner was only partially cleared, before tipping over a Brian Barry-Murphy free-kick.
But Royce was caught flat-footed from the resulting corner as Hurst found space to head home Barry-Murphy's in-swinger from just a yard out.
Miller had a shot saved blocked shortly after the restart while Nutter was denied by Brown.
Royce then saved a 20-yard strike by Bury winger Elliott Bennett, but Bennett and Hurst combined for Bishop to score his second with a six-yard tap-in before Bishop returned the favour for Hurst to head home from a deep left-wing cross.
Gillingham missed out on a consolation when Miller saw his 73rd minute spot-kick saved by Brown, who was booked for bringing down substitute Mark McCammon.