In order to only allow certain hosting sites, you would need to update the expression in the Avatar profile field box from ^
http://([A-Za-z0-9/.~_-]+)\.(jpg|gif|png)$|^$ to whatever suits the hosting site you desire. Unfortunately I'm no good with this sort of rewrites. vBulletin gives a link to
http://au2.php.net/manual/en/function.preg-match.php and explains the rewrite system.
What I would try to do, is identify the pattern with the host you want to allow, and match it in the expression. For example to allow photobucket only (not tested)
^
http://[A-Za-Z][0-9][0-9]|.photobucket.com|([A-Za-z0-9/.~_-]+)\.(jpg|gif|png)$|^$