Jason Dodd signed off as caretaker manager of Aldershot by guiding them into the second round of the FA Cup.
The Shots took a deserved lead in the 14th minute when Kirk Hudson's low cross was buried by Louie Soares.
Shots doubled their lead just after the half hour when Scott Donnelly evaded two challenges and calmly finished.
In the dying seconds of the match, Bury's Stephen Dawson sliced a gilt-edged opportunity wide, ending the Shakers' nine-match unbeaten run.
Aldershot caretaker boss Jason Dodd told BBC Surrey:
"We were worried that they were going to go out there and it was an anti-climax.
"Just the way they went about it, the shape and body language, and everybody was hungry. And whoever is going to take the job was obviously watching today thinking "I haven't got too much to deal with.
"It's pleasing to move on, but different times and different circumstances it might have been different, but we've had a great time and we can only thank not just obviously the players but the staff aswell who've been immense for us"
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