Bully"Shooter" is linked with a default vBulletin User Group called "Banned Users". The software, in its current configuration, does not separate "temp-banned" users from "perma-banned" users. Instead, it allows staff members to set a time frame during which a user is placed in the "Banned Users" group...it can be for a couple of days or weeks, or forever.
I think (and this is mostly a guess, so take it with a grain of salt) that other "User Groups" could be defined and populated (something like "Temp-Shooter"/"Perma-Shooter"), and then Custom User Titles could (potentially) be assigned to those groups. The hitch, I think, would be linking the new user categories within the vBulletin software to automatically place the newly-banned user into the correct user category (Temp/Perma) to keep it user-friendly for the staff.
I suspect there would be significant coding required to accomplish this, and that would be an effort only the site owners could authorize.