Dale opened the scoring when Mendez-Laing pounced on a loose ball from Ian Henderson's blocked effort.
Mendez-Laing then nipped in between Ian Lawlor and Peter Clarke to double his tally and Rochdale's lead.
Former Bury defender Ashley Eastham wrapped up the three points when he leapt highest in the Shakers' box to head Michael Rose's corner past Lawlor.
Rochdale manager Keith Hill told BBC Radio Manchester:
Media playback is not supported on this device
"We wanted more penetration and we got it today. I think the game should have been put to bed before half time with the chances we created.
"I think it was all about control of the ball today.
"The plan worked but the players, more importantly, put in some practice and that's what pleases me most."
Bury manager David Flitcroft told BBC Radio Manchester:
Media playback is not supported on this device
"It's been a real tough week. I've got players out there who physically weren't really prepared for the game.
"It didn't look right and it didn't feel right.
"We've got to get the right bodies in now and make sure we've got enough covering in every position to get over the line."
Nathaniel Mendez-Laing's brace secured a comfortable victory for Rochdale over local rivals Bury in League One.