The visitors scored seven tries to complete a 36-10 win over the Bulls, having led 26-0 at the break.
Bradford's head coach told BBC Sport: "We had very little possession in the first half an hour. They got a good roll-on and we spent too much time near our own goal line.
"You can't afford to play against the main teams without the ball. At the back end of the first half we asked some questions. We opened them up but couldn't finish off.
"I was pleased with the fightback and in the second half we were able to trade sets but we need more quality than that to beat St Helens."
The loss leaves Bradford sixth in the Super League table.