You have to grant permission for your vBulletin IP access to your TS mySQL.
Here is a quick Google result
http://help.hardhathosting.com/question.php/87
I use cPanel which allows me just to enter the remote IP, usually mySQL only allows localhost connections unless an IP is specifically granted.
Really, if you can, you should have TS use your vBulleting database and skip the remote access; it will be faster and more reliable.