Bradbury watched Cherries book their place in the end-of-season shootout courtesy of an eventful 2-2 draw at Hartlepool on Saturday.
Cherries will battle it out with three from MK Dons, Peterborough, Huddersfield and Southampton to compete in the Championship next season.
And although their semi-final opponents are not yet confirmed, the picture could become clearer after Southampton have met Plymouth today.
A win for Saints would all but earn them automatic promotion alongside Brighton and condemn Huddersfield to the play-offs. Defeat or a draw for Nigel Adkins's men would take it to the last day.
The semi-final line up is decided by league placings, with sixth meeting third and fifth playing fourth, both home and away. The final takes place at Old Trafford on Sunday, May 29.
Bradbury, whose team could finish sixth or fifth, said: It is a fantastic achievement to reach the play-offs and I fancy us to do well against anybody. We want to finish as high as we can and I don't mind who we play.
We have been the underdog ever since I have been here and have always risen to the occasion. I am quite looking forward to the fact that people probably won't give us a chance. It is all a bonus for us and we will give it a good go.
It is a massive achievement for everyone involved and credit must go to the players and everyone at the club. We always had an inner belief that we could do well as a group and have done so for the past couple of years.
Maybe our objective at the start of the season would have been to stay in the division. But we know that, on our day, we are as good as anyone else and feel we can be successful.
Cherries will be bidding to clinch back-to-back promotions after finishing last season as runners-up in League Two. The Dorset outfit has enjoyed a sharp upturn in fortunes under the chairmanship of Eddie Mitchell over the past two years.
Mitchell told the Daily Echo: Where we have come from has been down to hard work, not money. The team are part of the club and the club has been successful. It is not about individuals, it is down to everybody and is a team effort.
Hartlepool head coach Mick Wadsworth said: It is great to see the bigger clubs aren't dominating the play-offs. There are some really big payers in this division and it is fantastic what Bournemouth have achieved.
To come up last season and then do sensationally well this season is great credit to everyone at the club. They will have as good a chance as anybody else in the play-offs.
The Daily Echo and other media are currently not permitted to interview any Cherries players.