By making your vBulletin forum private you will prevent guest visitors from browsing and seeing the forum posts.

You can change the access permissions for the Unregistered / Not Logged users from your vBulletin admin control panel->Forums & Moderators -> View Permissions.

You should also alter them in your vBulletin admin control panel->Usergroups->Usergroup Manager->Unregistered / Not Logged In->Go.