Aaron Amadi-Holloway had the best opportunity of the game for Latics on the hour mark but his header was cleared off the line.
Athletic had to be wary in the final minute of the game as James Vaughan dispossessed Anthony Gerrard in the penalty box but George Miller forced a superb save from Connor Ripley.
That save extended Ripley’s clean sheet record for the season to 15 games.
Manager John Sheridan made three changes to his side which were beaten by Walsall last week.
In came Jamie Reckord, Chris Taylor and Ollie Banks in place of the suspended duo Brian Wilson, Lee Croft and the injured Rob Hunt.
It was a fast-paced start to the game with both sides intent on attacking.
Whilst both sides enjoyed spells of possession, Bury had the first chance of the game on 10 minutes as Taylor Moore volleyed into the side netting following a cross into the box from Greg Leigh.
Ryan Lowe felt he should have been awarded a penalty kick minutes later as he went over in the penalty area but the referee adjudged the striker to have dived and award Latics the free kick.
Bury fans were incensed by the decision, however, seconds later, Vaughan caught goalkeeper Ripley late to spark uproar from the home supporters.
It was a tasty opening with tackles but little chances in front of goal, but the game started to settle down after 20 minutes.
Lowe almost found a way behind the defence midway through the half but Gerrard recovered to block his shot.
The defender had a chance for Latics seconds later at the other end but his header was saved. Bury broke from that attack and midfielder Paul Caddis saw his shot from 25 yards deflected over the crossbar for a corner.
From the resulting corner, former Latics loanee Cameron Burgess attacked the ball but his back heel was saved on the goal line by Ripley.
Latics had a good chance on the half hour mark as the ball fell invitingly for Tope Obadeyi but the striker dragged his shot wide of the goal from 25 yards.
Bury continued to dominate possession as Latics were frustrated not to hold onto the ball better.
Five minutes before the break, Gerrard threw his body on the line to block a Bury shot as it remained goalless at the break.
It was a much better start to the second half for Latics who had two chances in the opening three minutes of the half.
After a corner into the box, Burgess looked to clear the ball but smashed it against Banks but fortunately for defender, the ball went wide.
Minutes later, a short corner was played to Obadeyi who cut inside and struck from the edge of the box but it deflected wide of the far post.
Whilst Latics were pressing for the opening goal, they had to be wary of the counter attack.
Lowe managed to find himself one on one with his defender but his cheeky effort towards the back post went wide.
Latics were taking the game to the visitors and earned a succession of corners which were defended well by the Shakers.
Just after the hour mark came a great chance for Latics, and it was great work from O’Neill. The midfielder hooked the ball into the box, he found the head of Holloway but his effort was cleared off the line.
It nearly turned sour for Latics seconds later as Bury broke up field and were presented with a two on one situation.
Vaughan advanced with the ball, attempted to pick out Lowe but McLaughlin was there to intercept the ball and clear the danger.
Caddis was the next to go close for Bury as he smashed across the face of goal but it went wide of Ripley’s far post.
With 15 minutes remaining, Latics were presented with an opportunity on goal as O’Neill was fouled on the edge of the box.
Obadeyi stepped up, struck the wall, but at the second attempt fired over the crossbar.
With the game petering out into a stalemate, Bury substitute Miller was presented with a golden opportunity to win the game for the Shakers.
Vaughan intercepted Gerrard in the Latics box, he pulled it back to Miller but the striker saw his opportunity saved by the legs of Ripley as the game finished goalless.
Oldham Athletic: Ripley, McLaughlin, Gerrard, Clarke, Reckord, Green, Banks, O’Neill (Flynn 80’), Taylor, Obadeyi, Holloway.
Subs not used: Kettings, Law, Edmundson, Fane, Osei, Erwin.
Bury: Murphy, Leigh, Burgess, Kay, Vaughan, Mellis (Bryan 60’), Barnett, Moore, Styles (Tutte 46’), Lowe (Miller 67’), Caddis.
Subs not used: Lainton, Pope, Hope, Pennant.
Goals: Oldham Athletic 0-0 Bury
Attendance: 5,776 (1,388 visiting supporters)