Bradbury's men were made to pay for a below-par opening period when Ian Goodison scored from close range to give the visitors a 41st-minute lead.
And although Danny Ings came off the bench to grab an equaliser, Rovers substitute Adam McGurk bagged a dramatic winner both goals coming in stoppage time.
Bradbury said: We were really disappointed. The lads were so dejected after getting back into the game late on and then conceding a second goal.
I thought we did okay in spells. But the first half was unacceptable and was nowhere near what we are about. I told the lads at half-time and they came out and were much better in the second half. We took the game to them and created a few more chances.
But the first half wasn't good enough. We are better than that and have proved it consistently throughout the season. We are about energy, work-rate and confidence and none of those was there in the first half, although they were in the second.
Bradbury, who felt Cherries should have been awarded a free-kick in the lead up to the Rovers winner, added: It is difficult to find a reason for the current run. Everybody was looking forward to the game and we wanted to put things right. We need to stand up and be counted because this is the type of pressure you should want. It is better to be under pressure to try to win promotion than it is to stay in the league.
It was also disappointing because the teams behind us lost as well. I don't know how many more chances we are going to get to increase the gap.
We went on a great run when I first took over as manager but I was under no illusions that it would last forever. Now is the time when myself and the backroom staff earn our money so it is up to us to lift the boys.
Bradbury made a double substitution at the interval with Marc Pugh and Lauri Dalla Valle replaced by Donal McDermott and Steve Lovell. And McDermott and Lovell combined to set up Cherries' goal for Ings, a second-half replacement for Adam Smith.
Bradbury said: I didn't think Pughie had been on top of his game and neither had Lauri. I wanted somebody to run in behind a bit more and stretch them off Steve Fletcher's knockdowns and flicks.
We tried to get down the sides and get balls to feet. Steve Lovell provided that more in the second half.
The goal will be great for Danny. He missed a few chances while he was in the team and I think he feels the pressure. He made a big impact so I was really pleased for him. I am sure it will do him the world of good.