Despite hitting the woodwork twice, Bury were unable to break down the Iron, who had Mark Duffy sent off in the first half for violent conduct.
Bury striker Shaun Harrad struck the post with a delicate free-kick and Efe Sodje clipped the crossbar with a header, all in the space of a minute.
Duffy was given his marching orders for an elbow on Patrick Cregg in the 31st minute, but Bury struggled to take full advantage in the League One clash.
In fact, the visitors should have scored when Jon Parkin played in Andy Barcham, but he chipped tamely into the hands of Bury goalkeeper Trevor Carson.
Bury's best chance came in injury time, but visiting goalkeeper Sam Slocombe reacted to deny Lateef Elford-Alliyu before David Amoo blazed the rebound wide.
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