The only goal of the match was a spectacular effort from leading scorer David Syers whose 25-yard right-foot shot flashed into the net off the inside of the upright after seven minutes.
Fellow midfielder Tom Adeyemi missed a great chance to increase Bradford's lead when he was put through on goal after 29 minutes but was twice denied by keeper Adam Bartlett.
Jamaican international striker Omar Daley also saw his 30-yard shot rebound off the post in the 61st minute as Bradford sought an all-important second goal, but Hereford also caused anxious moments in the home defence.
Guillem Bauza twice tested keeper Lenny Pidgeley in the first half and the Bulls caused more problems late in the game as they pressed for an equaliser.
Source: PA
Source: PA