Striker Jake Speight put Bradford in front from the penalty spot in the 81st minute but with three minutes remaining Stuart Fleetwood scored a crucial equaliser for the hosts.
Barnet's defeat at Accrington means they are both mathematically safe from relegation.
Both sides had chances in the first half, with Fleetwood firing wide for the Bulls and striker James Hanson seeing his header saved.
But it was not until nine minutes from time that the deadlock was broken as Stefan Stam's foul on Hanson allowed Speight to fire home from the spot.
But Hereford rallied and Fleetwood rifled in a superb free kick to earn them a share of the spoils in the 87th minute.