The veteran utility man, who scored twice at Grimsby last season, continued to find Blundell Park a happy goal-hunting ground when he netted his first strike for more than a year yesterday.
His 42nd -minute header cancelled out Jamie Devitt's opener to put Cherries back on level terms against their relegation-threatened hosts. But goals from Michael Coulson, courtesy of a dubious handball, and Ashley Chambers either side of Liam Feeney's fortuitous strike condemned Cherries to a last-gasp 3-2 loss.
The Dean Court outfit's woes were only compounded by Jeff Goulding's sending off, just seconds after he had been introduced as a 70th-minute substitute.
Bradbury offered no excuses in his assessment of Cherries' performance.
The former Manchester City and Pompey star told the Echo: I was pleased to get the goal and it got us back in the game.
But the main thing was the result. We felt we'd come here and get a positive result but we didn't do that and I thought we were under par.
They made it hard for us and pinned us back, especially in the second half. We gave away corner after corner and, with the wind, it was difficult. Having said that, it was the same for both sides.
They are on a little mini-run, they have a bit of confidence and it is a tough place to come.
But I didn't think we were 100 per cent at it not for the lack of trying it was just that things didn't come off for us us.
There are no excuses. We're better than we showed yesterday that's the disappointing thing.
All we can do is learn from it and take it on for Saturday.
With Cherries still in the automatic promotion places ahead of next weekend's Dean Court clash against Accrington Stanley, Bradbury urged his team-mates to get back on track.
The 34-year-old added: We've got to try to take some positives out of it and learn from it. We've got to grow up quick if we want to be in the top three.
It's going to be a tight nine games now and we can't play like that week in, week out, because we'll be nowhere near it.