The original Bully (2006) save files do work with Bully: Scholarship Edition (2008/PC). Scholarship Edition added new classes (Biology, Geography) and new missions. Trying to cross-load saves will result in an instant crash or "Save Corrupted" message.
Before installing mods or updating your graphics drivers (which can sometimes corrupt older Rockstar titles), always manually back up these files. bully game save
Because Bully lacks a multi-slot autosave system (like modern Rockstar games), you should manually back up your after every chapter. The original Bully (2006) save files do work