bbPress.org

1) Activity stream
I suppose you talk about the BuddyPress activity stream here ?
If so, maybe this code could get you started (found it on the BuddyPress forum). It will block ALL new topics/replies, so if you tune that to your private forums, it could be what you are looking for.

// Filter bbPress from updating activity stream
function imath_activity_dont_save( $activity_object ) {
$exclude = array( 'bbp_topic_create', 'bbp_reply_create');
// if the activity type is empty, it stops BuddyPress BP_Activity_Activity::save() function
if( in_array( $activity_object->type, $exclude ) )
$activity_object->type = false;
}
add_action('bp_activity_before_save', 'imath_activity_dont_save', 10, 1 );

2) To limit access to /forums, create a page with the slug /forums and add in that page what you want (a bbPress shortcode or just text). The creation of this page will prevent the standard forum index page to come up. Of course using any ‘members’ plugin, you could then e.g. make sure only admins could access.

Pascal.