Bore, who lined up against Glenn Hoddle Academy in the EC Group Cup, has been invited back to face Cardiff City in tomorrow's pre-season friendly at the Seward Stadium (1pm).
The 23-year-old is currently a free agent after turning down fresh terms to extend his stay with hometown club Grimsby, although the Mariners would be entitled to compensation should he sign for Cherries.
Bradbury, speaking to the Daily Echo following last night's 2-2 draw at Winchester, said: I am hoping to get Peter down for the Cardiff game. I think he has got good potential and, although a few clubs are after him, I know he would like to come to us. He enjoyed it when he came down, he liked the way we played and he got on well with the lads.
Bradbury is today expected to make decisions on trialists Jordace Holder-Spooner, Sofiane Choubani and Ivan Forbes. Choubani and Forbes both featured against Winchester, although Holder-Spooner was ruled out due to a hamstring problem.
Portsmouth defender Lewis Tallack, Dorchester's Gary Bowles and Polish trialist Szymon Sidorowicz also turned out at Winchester where Lyle Taylor notched his fifth goal of pre-season to give Cherries the lead.
However, a late brace from Darryl Phillips saw the hosts hit back before a fine finish from substitute Elliot Ward earned Cherries a draw, with teenage goalkeeper Jordan Seabright catching the eye for Bradbury's men.
Bradbury said: It was a worthwhile exercise and some of the younger boys did very well, as did a couple of the pros.
Cherries: Seabright, Hester (Tallack, h-t), Nelson (Strugnell, 72), Sidorwicz, Bowles, Forbes, Wakefield (Ward, 60), Campoy, Choubani (Parsons, h-t), Stockley (Moth, 72), Taylor.