What else is running on your site: for example, do you have anti-spam tools such as Akismet in place?
Something that is often worthwhile is troubleshooting by deactivating all other plugins and switching to a default, unmodified theme: if you do this and things work as expected, it would indicate that the problem is being introduced by one of those other components (or by a combination of some of those components).
OK, and are you in a position to take those testing steps a little further and deactivate everything except bbPress (and also switch to a default theme)?
If you can do that, and things work, we then know the problem lies in one of your other plugins or with your theme and by reactivating them and testing you can probably figure out which one is the problem.
You could even do this ‘in reverse’ if you want to avoid disruption on your live site. This service has a funny name, but poopy.life is really useful for this sort of thing. Start with a brand new WordPress install (it’s free, though it will only stay alive for 24hrs) and add bbPress but nothing else. Confirm it works as expected, and then start adding everything else that you have on your live site: see if you can figure out what exactly introduces the problem.