I'm not too familiar with vBulletin myself, but according to this page
http://www.vbulletin.com/manual/install.html
you should open up config.php and change the following lines:
Code:
// username and password to log onto db server
$dbusername="root";
$dbpassword="";
Place your new password between the quotations after $dbpassword and make sure $dbusername is still correct.
Hope I'm not completely off base here.