I always get confused about the relationship since WP and bbP are SSO 🙁
The new public registration is always WP Subscriber, who is subscribed to bbP Announcement forum by bbP Toolkit. This is the only user role that needs to go to bbP edit-profile page. The other role in use is the Contributor which should jump to wp-admin/profile.php instead of bbP edit-profile. I hope this is somewhat clearer.