The Bees twice fell behind to goals from James Hanson and Zesh Rehman but showed their battling qualities with John O'Flynn and Hughes earning them a deserved point.
Bradford flew out of the traps, and Hanson had already gone close before he broke the deadlock in the 14th minute. Former Blackpool midfielder Michael Flynn's driving run and cross found Hanson at the far post and he poked the ball past Jake Cole.
Chances were few and far between before the break, but after the interval the match came alive when O'Flynn equalised, heading in Kenny Gillett's cross.
O'Flynn and Ismail Yakubu then wasted great chances to fire the Bees in front but they failed to test Simon Eastwood.
Bradford were on the ropes, but they bounced back to storm back in front after 70 minutes when Rehman smashed home James O'Brien's corner. But back came Barnet and they deservedly drew level nine minutes from time when midfielder Hughes headed in O'Flynn's cross.