Mike Jones broke the deadlock in the 37th minute with his third goal of the season and that proved enough to give the Shakers their first win in five games.
The game was given the go-ahead after two pitch inspections and both sets of players looked uneasy on their feet in the freezing conditions.
Barnet had an early scare when Andy Morrell put Jones in behind the Bees' defence and although Albert Adomah appeared to bring down the Bury winger, a free-kick was not given.
Bury named Mark Tyler in goal after he signed from Peterborough on a one-month loan deal and he was tested by a 20-yard effort by Michael Leary.
Veteran Barnet striker Paul Furlong then volleyed over from a Tommy Black corner, while Bury's Andy Bishop fired straight at Ran Kadoch from distance.
Furlong turned Leary's left-wing cross straight at Tyler just after the half-hour mark, but Bury had enjoyed the bulk of possession and took the lead when Jones turned the ball in at the far post after Morrell flicked on Elliott Bennett's right-wing cross.
Furlong was off-target again just after the restart before Bishop was denied by Kadoch after combining well with Jones down the Bury left.
The Barnet keeper then produced a fine save in the 65th minute to tip over Morrell's close-range header from Bennett's right-wing cross.
The visitors responded with Black firing straight at Tyler from the edge of the box, while Furlong deflected a Neal Bishop strike narrowly wide.
Bennett should then have sealed it for the Shakers when he fired too close to Kadoch after being put through by Morrell's flick, but they managed to hold on despite a nervy finish.