Jimmy Smith opened the scoring in the ninth minute when he slammed the ball home from 12 yards after Mathieu Baudry had flicked on a corner by Dean Cox.
That goal came against the run of play with Bury squandering three chances in the opening three minutes when Tom Soares twice failed from eight yards and Nicky Ajose then fired wide from 10 yards.
Bury's woes increased when David Mooney doubled the lead in the 34th minute after some woeful defending. Lloyd James played the ball into the box and Smith then swept it onto the unmarked Mooney to notch his 13th goal of the season.
The visitors continued to throw away chances after the interval with Steven Schumacher and Andy Bishop again failing to find the target when well-placed.
And it was the home side who came closest to adding to the scoreline when Mooney and Charlie MacDonald saw efforts scrambled off the line.