Dragons midfielder Mark Jones provided one of the few attempts on goal, letting loose a 30-yard drive that Bury keeper Kasper Schmeichel dived at full length to turn away for a corner.
Jim Whitley was next to try his luck, hitting another long shot that went straight into the keeper's arms.
From another Wrexham raid Sam Williams put Matt Crowell through for a wayward strike off target.
Wrexham supporters called for a penalty on 23 minutes when Schmeichel raced out to intercept Matt Derbyshire just inside the area and the young home striker went down. But referee Nick Fletcher merely booked the home player for diving.
Both sides pushed up more in the second half and Bury were out of luck when Colin Marrison saw his shot blocked on the line by Shaun Pejic.
From Bury's next raid Dwayne Mattis was clean through on an unguarded net and fired over the crossbar.
The Shakers' player was out of luck again just after the hour as he beat keeper Mike Ingham and saw his shot hit team-mate Tom Youngs on the line before bouncing wide.
Wrexham enjoyed a spell of late pressure and would have scored but the hard working John Fitzgerald scrambled back to clear from Sam Williams.
Dean Bennett tried a long range volley that went straight at the keeper and Derbyshire headed into Schmeichel's arms from a defence splitting cross from Mark Jones.
With time running out Wrexham made and missed their last chance, Derbyshire heading wide from Levi Mackin's cross.