It looks like you are using
This Hack to show it on all your pages.
If that is the case, try this.
Remove this bit of code from the "vBShout [Template Alteration]" plug in in your plug in manager in your ACP.
PHP Code:
$Position = '<!-- / nav buttons bar -->';
$vbulletin->templatecache['navbar'] = str_replace($Position, $Position . '<br /> $Shoutbox', $vbulletin->templatecache['navbar']);
Then you will have to go in and add this code to all pages you want to add the shout box to.
HTML Code:
<if condition="$show['member']">
$Shoutbox
</if>
That should show it only to members.
EDIT:
Errrm... isn't there a way to ban certain usergroups from seeing the Shout Box in the admin cp?
EDIT 2:
I remember why I did this on my forum - it was giving me and error when I tried to ban members from seeing the shout box. But, if the setting in the ACP works for you then you should probably use that method, if not, mine should work.