I would just turn off registration (remove all links to the registration form) and then user something like this plugin to create the user accounts:
That is an old plugin but instructions on how to make it work for 1.0.2 are in the comments.
I thought there was a plugin by user zaerl that could help but I can’t find it right now.
No no. My plugin just remove all fields in registration page except user name and email. Nothing more.
One of the major things that bbPress doesn’t do well is make the forum easy to moderate in anyway. 7 clicks and 4 pages to delete 1 user, and no ability to mass delete is mental.
If you have a forum that needs constant moderation for any reason, bbpress might not be the best solution sadly