Reluctant? Harry saved his life and, more important, his daughter's life (also, other kids and the daycare lady). And Murphy, who was working with Harry, gave her life for it. I think Bradley would be very grateful and help in all what he can.
What we know about Bradley is that he's a good fighter, he's in Internal Affairs rather than being a beat cop or SI, he's got a young child who had to stay at a night nursery while he was on shift, which means he may be a single dad, and he's already seen a bit of the supernatural and wanted to walk away.
I could easily see him thanking Harry softly and convincingly, and then just as quickly telling him he'll do nothing that might leave his kid an orphan.
Maybe angelic daycare at the Carpenters might change that, but seeing Michael be retired and crippled, and seeing Butters and Sanya working and crippled, and he's likely to say a respectful but firm No.