Unfortunately, I had a cold and was unable to reply. Let me update my current setup, answer questions and provide visual bugs.
I'm using WP 3.5, BBpress 2.2.3, Ultimate TinyMCE 3.9. as well as the plugins mention initially (bbPress Like Button, Duplicator, Global Hide/Remove Admin Bar Plugin, Theme My Login, and User Meta).
How do you have the private forums set up? Are they Open or Closed?
They are open.
Is the visibility set to Private?
Is there a parent forum?
Two forums, both are parent forums with no child.
I've tried it from the admin level to the subscriber level and it all works like it should.
Unfortunately, only Admin level works for me at this time. All other levels are unable to see the private forum at this time.
What "small admin menu" are you referring to?
This menu at the beginning was not visible. But it is not the case anymore for version 3.9.
The bug was notified to me by the users as they were not able to post on the private forums since it could not be found. As an admin I guide my users through normal troubleshooting (ie password reset, cache flush, cookie removal, etc.). Then I pull my hair guessing where the issue lies but as admin I was not able to see it. So, I created a user which I granted forum access. Alas, 404 error again the forum was not visible to the user unless he was an Admin. I try changing the theme same issue the private forum was not visible. So, it hit me it could be your plugin. Sadly, once disable the plugin the private forum was once again visible to all registered members.
On a positive note: The toolbar works on most or all Twenty (10, 11, and 12) Themes if memory serves right but I'm unsure. I do remember being happy about that in particularly.
Unfortunately, I can't provide a more technical insight but I think Ckone seems to have a better idea and mentions details I have read before in other posts.