Three points would have been perfect for both teams with just six games remaining in the League Two scrap for survival.
But neither Chris Casper's nor Brian Horton's teams respectively could capitalise by finding full points to lift them up the table.
Midfielder Danny Whittaker fired over after just 32 seconds as Macclesfield had the first chance of the game, before at the other end Ian Ross, one of Bury's four deadline day loan signings, saw a right-foot curler fly inches over the crossbar.
Ross fired high and wide moments later, before Matty McNeil had a shot saved by Bury keeper Kasper Schmeichel and then Paul Harsley went close with a dipping volley.
Marcus Richardson had a goal disallowed for offside midway through the first half, before Lewis Gobern, another loan recruit, went close with a powerful right-foot shot from the edge of the box.
Gobern nearly gave the home side the lead on the stroke of half-time, but although his trickery in the box baffled Macc's defence, their goalkeeper Tommy Lee saved smartly with his legs.
Bury started brightly in the second half and with just 58 seconds gone, Lee was forced to make a good stop from Brian Barry-Murphy's testing free-kick from distance.
Four minutes later striker Jon Daly, who scored Bury's winner against Stockport last Saturday, saw a powerful right-foot shot deflected for a corner.
Whittaker forced Schmeichel to save well with a vicious volley shortly after the hour mark, before Tom Youngs fired over for Bury in front of the Manchester Road end.
Ross saw a right-foot shot fly wide of the left-hand post with 19 minutes to go, before eight minutes from time veteran midfielder Dave Flitcroft fired over from a tight angle 20 yards out.
Substitute Colin Marrison had a shot deflected for a corner as pressed for an opener until, with two minutes left, Gobern had a penalty turned down by referee Trevor Parkes.
The midfielder was tripped in the box by former Bury defender Danny Swailes, but Gobern was handed a yellow card after Parkes deemed he'd dived.
Gobern came close to getting sweet revenge in the dying seconds of the match, but his thunderous left-foot shot flew agonisingly wide of the left-hand post.