Welcome to Best Board's Support board!
To make a forum private you have to log into your Admin Center-Edit Forums-pick the forum you want to make private and you can go as far as setting it to be hidden and 'Editing Users' in by giving them the ability to see the hidden forums.
Check this link out:http://bb.bbboy.net/man/admin.html#admin_button_edit_forums
In there you'll see all the different 'Forum Settings' you can change and it goes over them in more depth. If you want to make it Hidden you will have to take the extra step to edit users who you want to see it and post in it-select them all, and select 'Set Hidden Forum Viewing Ability' and then you'll see the check boxes to empower the selected users to be able to see it-then repeat and 'Set Private Forum Access'. Here is a link on that from that same tutorial:http://bb.bbboy.net/man/admin.html#admin_button_edit_users
Hope that helps!