The visitors' first-half performance was controlled and they should have at least been two goals to the good at the break.
The missed chances could have made them pay as the Daggers came out a different team in the second period and felt they deserved a point from the game.
In the early exchanges Andy Williams and Jamie Pitman created chances for the Bulls to take the lead with Pitman's effort coming from a well-worked free-kick just outside the penalty area.
The visitors did open the scoring on 12 minutes from Williams after sustained pressure on the Daggers goal.
The lively Guy Ipoua was denied by a great Tony Roberts, but Willliams was on hand to force the rebound home at the far post to score after his first attempt had hit the woodwork.
The lead could have been doubled five minutes before the break. Alex Jeannin's cross to the far post found Jon Brady completely unmarked, but his half-volley flew wide.
The opening period finished on a high for the Daggers when Paul Benson went close to scoring. Craig Mackail-Smith's cross was inches over Benson's head as he arrived late at the far post. Craig Mawson saved seconds later from Benson's close-range header.
The woodwork was hit for the second time in the match when Pitman's right-foot drive hit the post and it was Lee Goodwin who cleared the danger.
The Daggers continued to search for an equaliser but the Hereford defence held strong.
In injury time the Daggers had a corner and it was their goalkeeper Roberts who arrived to win a header, but Mawson denied him.