An uninspiring first half lacked little goalmouth action although it was Bury who carried slightly the greater threat.
Joe Skarz's curling 25-yard free-kick forced a scrambling save from Chris Weale, diving low to his right, while Steve Schumacher's shot was well blocked by Yado Mambo, making his first start for Shrewsbury since arriving on loan from Charlton.
Shrewsbury carried little threat with a Joe Jacobson free-kick which cleared the bar as good as it got for Graham Turner's side.
The second half was only marginally better with Bury, without a win in their last 12 games in all competitions, nearly making a breakthrough when sub Andy Bishop hooked a close-range effort on to the top of the bar.
Shrewsbury perked up a little when Luke Summerfield and Steve McGinn were sent on in a double switch.
And Dave McAllister was close to firing them ahead when his deflected 25 yarder looped up against the top of the bar.
McAllister then forced Trevor Carson into his first save of the game five minutes from time before Bury almost snatched it right at the death when Ethan Ebanks-Landell had an effort scrambled off the line.