bbPress Notify (No-Spam)
bbPress Notify (No-Spam), aka bbPNNS is a powerful notification plugin designed to send out alerts to all users belonging to selected roles. By default, however, it does not come with support for filtering out people who do not have access to see a given forum.
Requirement: bbPress Private Groups
bbPress Private Groups is an excellent plugin that provides the ability to assign users to groups and thus control forum access. The bbPNNS Private Groups Bridge plugin makes sure that bbPNNS will comply with the rules set by admins, and will not deliver alerts of new topics and replies to people who do not belong to the correct groups.
As a bonus, if a user needs to be logged in to read a topic or reply, the plugin will automatically present them with the login screen and redirect them back to the post after they log in.
There are absolutely NO settings required for this to work. Simply activate it and it will make bbPress Notify (No-Spam) play nicely with bbPress Private Groups.