The Shakers striker hit 25 goals last season and although he failed to register in pre-season, the 25-year-old struck three minutes before the break to give the hosts a deserved victory at Gigg Lane.
Brentford started strongest with Marcus Bean going close before new Bury goalkeeper Wayne Brown denied Alan Connell at his near post from a Marvin Williams cross in the fourth minute.
The visitors threatened again when Nathan Elder headed goalwards from another Williams cross in the 16th minute but it was comfortable for Brown.
Elliott Bennett was looking dangerous down the Bury right and the hosts almost opened the scoring in the 21st minute, after Ben Hamer failed to punch a Michael Jones cross clear. Ben Futcher knocked the ball back in and captain Paul Scott headed agonisingly wide with Hamer beaten.
Futcher headed wide from a Brian Barry-Murphy corner on the half-hour mark before Jones dragged a 12-yard effort wide after being released by Bishop's lay-off.
Stephen Dawson was called upon to clear the ball off the line for Bury after Elder directed Kevin O'Connor's corner goalwards, but Bury broke the deadlock three minutes before the break.
Bennett played the ball forward for Glynn Hurst, whose lay-off found Jones and the Bury winger played the ball right for Bishop to cut inside and fire left-footed past Hamer from 16 yards.
Brentford came out sharper again at the start of the second half and Bury left-back David Buchanan cleared from Williams at the back post, before Elder flashed a header just over from Sam Wood's left-wing cross on the hour mark.
Hurst should have sealed it for Bury with 20 minutes left but hit a post after being released by the impressive Bennett.
Brown had to be alert to save a 25-yard drive from Connell shortly after, while Hamer saved a similar strike from Jones and O'Connor blazed over at the death.