[@robin-w Moderator 7 years, 9 months ago]

the first ‘forums’ is the sub domain where he has installed it (what you call ‘in its own folder) so that cannot be changed.

The ‘/forums/’ is what bbpress uses, you can omit that in the sub-domain wp installation

dashboard>settings>forums>fourm root slug, and untick the ‘Prefix all forum content with the Forum Root slug (Recommended)’

That might achieve your first objective, but probably what you really want is the forums within your site, unless your site is massively complicated or your forums are huge, there is no reason not to have bbpress within your main site