The Shakers went in front in the second half through on-loan Sheffield Wednesday striker Danny Reet but the home side rallied and were rewarded with a Ben Strevens headed equaliser and almost clinched all three points in a late onslaught.
The first half honours mainly belonged to the home side with Shakers' keeper Neil Edwards forced into several top drawer saves from Giuliano Grazioli, Paulo Vernazza and Liam Hatch.
The former Stockport and Rochdale shot-stopper was in fine form and earned deserved his praise from manager Chris Casper.
'Neil was excellent and kept us in the game with some superb saves,' he said. 'We were a little bit loose and switched off at times but he kept us in it.
'With so many youngsters in the squad it's important to have someone of Neil's experience.'
Bury's best efforts came courtesy of a long range Nicky Adams shot and a Reet header but both were easily dealt with by Ross Flitney in the Barnet goal.
In the second half Reet became embroiled in a running battle with Ian Hendon and that tussle, coupled with the introduction of lively substitute Jake Speight, ignited the game.
New signing Speight went close with a low shot from distance before the Shakers took the lead when Reet rifled home from 25 yards after a swift Bury counter-attack involving Simon Whaley and Speight.
However, Barnet rallied and disappointing slack marking at the back allowed Strevens to head home Nicky Bailey's corner with six minutes remaining.
Whaley had another long range effort saved but it was all Barnet at the death and substitute Jason Norville blazed wide when presented with a chance to give his side the three points.
Casper added: 'I was gutted for the lads they worked hard. We had two or three good chances to kill the game off but Barnet had theirs too and a draw was probably a fair result.
'These type of games are when the young lads have to turn into men, it was a physical game and we didn't get much protection, but that's football.
'The players put their bodies on the line and got the point and there were one or two gashed faces at the end of it.
'We were tactically excellent and very brave.'
With newly installed assistant boss Ian Miller in the dugout for his first game Casper declared himself well pleased with his latest appointment who was number two to Colin Hendry at Blackpool until last week.
'It was the first time I'd had Ian by my side at a match, he's good tactically and he's inspirational too.
'He's also someone I can trust, which is important to me.'
BURY: Edwards, Whaley, Scott, Challinor, Woodthorpe, Kennedy, Adams (Speight 55), Barry-Murphy, Buchanan, Youngs (Parrish 90), Reet (Tipton 82).
Subs not used: Dootson and Quigley.
REFEREE: Mr T. Bates (Staffordshire)
ATTENDANCE: 1,796
^^ Taken from the Bury Times