Defender Ryan Cresswell's goal - his first for the club - gave Bury their first win in four matches.
Cressell rose at the far post to convert a free-kick from Michael Jones, who had earlier missed a good chance.
Jones wasted a one-on-one with County goalkeeper Russell Hoult and later smashed a shot against the post.
Bury's Andy Morrell and Elliott Bennett also missed chances before Myles Weston went close to equalising when he grazed the post in the closing stages.
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