BuddyPress.org

@mirgcire
http://premium.wpmudev.org/manuals/the-buddypress-manual-2/

@mirgcire
That one may work you may also wanna try out these as well:
https://wordpress.org/plugins/bp-registration-options/
https://wordpress.org/plugins/invite-anyone/
https://wordpress.org/plugins/buddypress-registration-groups-1/
These may help get you close to what your looking for!

@mirgcire
You cant send invites until you have friend connections even if your the owner of the group. However if Tom owns a group that is set to public then Jane can join that group.

@mirgcire
As of BP 1.7+ bbpress is a seperate install. Try following the below instructions.
1.) Go to dashboard/settings/buddypress/components and check the box “User Groups”
2.) Install and activate bbpress.
3.) In the front-end go to the groups page and click the button “Create a Group”
4.) Give the group a name and description, click “Create…[Read more]

@mirgcire
Not sure if you have viewed this page but it is more current.
https://codex.buddypress.org/user/setting-up-a-new-installation/installing-group-and-sitewide-forums/