Create a private forum with bbPress

This is probably your best option:
http://www.adityanaik.com/projects/plugins/bb-private-forums/

It hasn’t been updated recently, but has been used by several people with the most recent update of bbPress, so it should be fine.

Or, if you want all forums to be private, what I’ve done is add a conditional statement to the top of the page. (If logged in, show the forums; if not, show the login page.)

this is so easy;

http://codex.wordpress.org/Function_Reference/is_user_logged_in

<?php
if ( is_user_logged_in() ) {
    echo 'Welcome, registered user!';
} else {
    echo 'register and login!';
}
?>