Robin W

This Plugin IS NO LONGER MAINTAINED
use https://wordpress.org/plugins/bbp-private-groups/
This plugin displays private forums titles to non logged-in users in main index.
This allows non logged-in users to see that forums exist, but have no acces to these.
If selected by a non logged-in user, the use is sent to a page (determined in settings), allowing the admin to determine what information is given, eg login, registration, text etc.
It also has the options to
display forum content (descriptions) for sub forums
remove the prefix ‘private’ from all private forums
Works with bbpress 2.5.4

Private forums visibility

For bbPress - displays private forums titles and optional descriptions to non-logged in users, and optionally hides the prefix 'private'

dFactory

<a href="http://www.dfactory.eu/plugins/bbpress-notifications/" rel="nofollow ugc">bbPress Notifications</a> allows you to automatically send email notifications to specific users when new topics or replies are posted. It integrates seamlessly into WP, by adding new section to bbPress settings page, where you can configure your notifications.
For more information, check out plugin page at <a href="http://www.dfactory.eu/" rel="nofollow ugc">dFactory</a> or plugin <a href="http://www.dfactory.eu/support/forum/bbpress-notifications/" rel="nofollow ugc">support forum</a>.
<h4>Features include:</h4>
<ul>
<li>Send notification when New Topic is published</li>
<li>Send notification when New Reply is published</li>
<li>Specify email addresses for notifications</li>
<li>Design email templates with a number of shortcodes</li>
<li>Available shortcodes: [blogname], [reply-title], [reply-content], [reply-excerpt], [reply-url], [reply-author], [topic-title], [topic-url], [topic-author]</li>
<li>.pot file for translations included</li>
</ul>

bbPress Notifications

bbPress Notifications allows you to automatically send email notifications to specific users when new topics or replies are posted.

Private forums visibility vs bbPress Notifications