A goal in each half ended City's month-long spell of bad form, and though Bury sporadically put on the pressure, they rarely threatened.
City started brightly, with Stuart Elliott and Andy Dawson putting in some dangerous crosses from the left wing.
After ten minutes, Elliott put a 15-yard shot wide, before Dawson's long-range effort went well over the bar.
After 15 minutes Phil Gulliver headed wide during a momentary lapse in City's defence with keeper Paul Musselwhite nowhere.
But just two minutes later Elliott was fouled just outside the box and Marc Joseph's free-kick was spilled by Glyn Garner. Jason Price was alert to run onto the rebound and hammer it home from a couple of yards out.
After 25 minutes a powerful shot from Lee Connell went just wide as Bury began to come into the game and force City into their own half.
After 38 minutes Connell ran clear only to see Musselwhite pull of an excellent save at his feet right on the edge of the area. A minute before half time a looping shot by Gareth Seddon was saved by Musselwhite.
Barely a minute into the second half, Price ran clear on the right and flung in a cross to Ben Burgess who had time to control the ball and hammer a shot into the net.
City seemed fired up by Burgess' goal, as was the goalscorer himself, who saw two more efforts go close in a bid to add to what was his first home goal since October 12.
After 63 minutes an excellent effort from Elliott on the left-hand side of the box thundered off the crossbar and ten minutes later a header from Elliott was collected at the second attempt by Garner.
Bury began to pressurise again but City's defence was always up to the job and the final killer ball just never came from the Shakers.
Five minutes before time Burgess made a mess from what should have been an easy chip, so City had to be content with their 2-0 victory.