A wonder goal from Omar Daley put City 1-0 up against Bury at half-time.
The Jamaican volleyed a looping cross by Tom Adeyemi from ten yards out which almost broke the back of net, giving goalkeeper Cameron Belford no chance.
It gave City a deserved lead after they had the better of the first half, despite Bury making the more impressive start.
Ryan Lowe twice went close to putting the visitors in front after just six minutes.
But the Bantams came back into it, going close through Jason Price and Tom Adeyemi before Daley’s stunner.
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