The hosts took a 37th-minute lead through Damien Mozika before Andy Bishop equalised with a 46th-minute penalty and the Shakers had chances to claim all three points.
Bury made a lively start although the first effort on goal didn’t come until the 25th minute when Bishop had a header comfortably saved by John Danby.
The Chester keeper also claimed an Andy Morrell header before Kevin Ellison’s volley forced a diving save from Bury keeper Wayne Brown.
Danby then tipped over a fine long-range strike by Stephen Dawson, but Mozika opened the scoring against the run of play from Ryan Lowe’s pull-back.
Bishop sidefooted home from the spot after Morrell was brought down by Paul Linwood, and both Bishop and Morrell wasted glaring opportunities to go in front.
But Bury were grateful for a point after Paul Taylor dragged a 16- yard strike wide while James Vaughan’s long-range effort almost caught Brown off guard.
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Pint of Blue, please!, Audenshaw (08/09/2008 at 10:16)
I've got to say that the quality of football from Bury was exceptional, as was your fantastic away support. The support from your left back to Jones on the left was noted by all of us.
We could see why you're unbeaten, as you reduced Chester to long range efforts that were comfortably dealt with by Brown in goal.
Hopefully, from a Man City fan, it's onwards and upwards for The Shakers, especially under Alan Knill.
Best of luck for the rest of the season.