Two first half half goals from Oli Johnson did the damage for a Bradford side who went into the game with two defeats out of two and were bottom of the division last season.
To their credit, Hereford looked a threat going forward in the first half and went close through a thunderbolt Luke Haines effort that rattled the crossbar.
But the Bulls were very poor in the second half and didn't look like getting back into the game. That is now just one league goal in three games, and that was from the penalty spot. Hereford's lack of proficiency in front of goal is clearly a concern, and after looking solid in their first two games defensively, the way the goals were conceded tonight is also a concern.
Hereford manager Josh Gowling named an unchanged side from the team that gained an impressive win at Guiseley in their last outing and would have been confident in picking up another three points.
However, it was the away side who came out of the traps the quickest, and with barely a minute on the clock, went ahead when Johnson tapped home Brad Dockerty's low cross.
Despite not creating too many openings, Hereford still looked a threat whenever they ventured forward, with Lenell John-Lewis leading the line well.
And they almost did draw level in spectacular fashion in the 23rd minute when Luke Haines tried his luck from distance. However, his effort rattled against the crossbar.
Back at the other end and Paul White had to be alert to push the ball away from danger after he had initially saved Dockerty's low free kick.
Just after the half-hour mark, John-Lewis went close to making it 1-1 when his shot was cleared off the line before Tom Owen-Evans had an effort saved.
However, the sucker punch arrived in the 38th minute when Johnson weaved his way through the Hereford defence to score and put Bradford 2-0 up.
The Bulls still had chances to pull a goal back before the break through Andrai Jones, John-Lewis and Finn, but all three were denied.
Gowling made a double change at half time, bringing on Kelsey Mooney and Yan Klukowski in an attempt to get back into the game.
However, the Bulls were way off the mark and it was Bradford who were in complete control and could easily have extended their lead.
Johnson went close to sealing his hat-trick in the 73rd minute, while Hereford's efforts were merely 'half chances'.
Overall, Hereford fans will be disappointed with how the team played in the second half, especially as they looked a threat in the opening 45 minutes.
Next up is a long trip to Spennymoor on Saturday.
- Hereford: White, Hodgkiss, Haines, Wright, Grimes, A Jones (Klukowski 46), Owen-Evans (Mooney 46), Finn, John-Lewis, Lloyd (Coke 75), D Jones. Subs not used: Digie, McQuilkin.
- Bradford (PA): Atkinson, Ross, Boyes, Marriott, Havern (c), Lund, Johnson, Hibbs, Nowakowski, Dockerty, Clee. Subs not used: Toulson, Fawcett, Windass, Downing, Lyons.