Cleveland Taylor, on loan from Bolton, had the ball in the net for the Iron after 26 minutes but Steve Torpey was penalised for a foul on Glyn Garner.
Scunthorpe were struggling to put anything together at all and had lucky escapes when Danny Swailes and skipper Lee Duxbury went close.
When Thomas Kennedy drove in a testing ball from the left Phillip Gulliver, on loan from Middlesborough, headed the ball onto the angle of post and bar and out for a corner, much to Scunthorpe's pleasure.
Scunthorpe introduced striker Paul Hayes after the break and he quickly flashed a header wide of the mark and Ian Kilford also went close.
Garner came to Bury's rescue when he turned away a free kick from Jeff Smith and Swailes blocked a shot from Hayes.
Hayes was a real thorn in the Shakers rearguard, and he pivoted well to strike a shot which flicked the crossbar.
Bury came strongly towards the end with Swailes again going close and Jon Daly had the ball in the net near the end but once again his effort was ruled out of order