The closest the hosts came to a breakthrough was Stuart Lewis' second-half volley which struck the post.
Bury hung on for a point to keep their own hopes of a top three finish intact going into the final game of the season next weekend.
The prospect of automatic promotion attracted more than 8,000 to Priestfield, easily the biggest league crowd of the season at the Kent club.
The home side shaded an entertaining but goalless first half, creating the bulk of the chances.
Andy Barcham, Mark McCammon and Josh Wright all had efforts on goal, but Wayne Brown was relatively untroubled.
The biggest problem for the visiting shot-stopper was his footwear, looking unsteady even after changing his boots midway through the half.
At the other end, Andy Bishop and Glynn Hurst provided the main threat. The pair linked up well to create the Shakers' only effort on target before the break, with Hurst forcing a good save from Simon Royce low to his left.
Shakers boss Alan Knill admitted before the game he would be content with a point and after the break Bury looked happy to sit back and absorb the pressure.
Gillingham accepted the invitation and spent long spells in the second half camped in the opposition half.
Dennis Oli's introduction from the bench on the hour gave them added impetus as Bury were pinned back.
Again the Gills struggled to test Brown until Lewis' superb 72nd minute volley beat the keeper but swerved at the last moment to cannon back off the upright.
It was the final clear chance, forcing Gills to re-focus on the play-offs, while Bury will hope to overtake Exeter on the last day of the season.