bbPress.org

With integration, you are sharing the wp_users table. Even if bbPress and WordPress are in different databases, there is going to be some shared data – that’s what the integration does. So having bbPress and WordPress in different databases doesn’t actually help with that. If you have them in the same database, just drop the bb_ tables and edit the users to remove any bbPress users. I don’t think using different databases helps you down the road.