A draw was just about a fair result but though both sides had opportunities to clinch a win.
Kasper Schmichael produced two great saves to deny Town skipper Richie Barker while opposite number Jason White also displayed exemplary handling.
"We had our moment but the quality of the game was poor," said Mansfield manager Peter Shirtliff.
"What disappointed me most was our poor quality on the ball individually. At least we're safe and we've managed to turn the club around clawed our way to mid table mediocrity.
"But I'm not settling for that and I want players next season who also want to do better."
Matt Tipton, formerly with Mansfield at the start of the season, wasted a sixteenth minute chance when he headed wide from a perfect Louis Gobern cross. He put another effort wide at the target and then directed another header straight at White.
Schmeichel's best moment came after seven minutes when he clutched Barker's header on his goal line. And in the closing minutes he kept out Barker's second header after good work by substitute Adam Birchall.
Bury skipper Dave Challinor said: "Their wasn't a lot in the game but it would have been nice to finish off with a win.
"We had chances in the second half but we didn't get the break infront of goal.
"Now we probably need a point from the last game but at least we've got the situation in our own hands."