How to make a vBulletin forum private?
By making your vBulletin forum private you will prevent guest visitors from browsing and seeing the forum posts.
To change the access permissions for the Unregistered / Not Logged users, go to your vBulletin admin control panel > Forums & Moderators > View Permissions.
Also, alter them in your vBulletin admin control panel > Usergroups > Usergroup Manager > Unregistered / Not Logged In > Go.