Visitors Southampton dealt a blow to their neighbours' promotion hopes and enhanced their own chances by claiming a 3-1 win in front of a capacity crowd at Dean Court.
Cherries looked on course for a positive result when loan man Lauri Dalla Valle volleyed them into an early lead.
But the hosts conceded a sloppy equaliser when Rickie Lambert was allowed to cross for Lee Barnard to head home.
Cherries saw a strong penalty appeal waved away and enjoyed plenty of possession, but it proved in vain when Dean Hammond handed his side the lead from close range. Lambert sealed the verdict with a superbly struck free-kick late on.
Despite the setback, Cherries' second defeat in a row, Bradbury was encouraged by his players' efforts.
He said: I thought for long spells of the game we were the better side.
I said to the lads they had to be proud of themselves for the way they conducted themselves and the hard work they put in.
If we had been given a penalty on Danny Ings, which we all thought was a penalty, at the right time, at 1-1, it could have been a different game. I thought the lads did brilliantly.
It was frustrating to let in three goals at home but, having said that, we could have had a few ourselves.
We hit the crossbar, we could have had a penalty and, on another day, Anton Robinson could have scored from the edge of the box as well. We had our chances too.
Opposite number Nigel Adkins was pleased but refused to get carried away.
He said: We got three points, scored three goals and the supporters went away happy. We move on to the next one.
It was a competitive game, the ball was bobbling about a little bit and there were a few oohs and ahs.
The game was a little bit lively. We weren't winning the first ball from their goal kicks and that allowed them to drop on to too many second balls. That led to their goal from the throw-in.
We allowed them to get into the game a little too much really.
But you have got to grind away and that was what the players did. That is the way it is going to be from here on in, especially away from home. The pitches are lively and you have got to grind away.
We are in a good position, we have got a good group of players and we were pleased we got a victory.
For in-depth reaction, match comment and pictures, see tomorrow's Daily Echo.