Below is a list of files which you should back up, once you have got a stable and satisfactory setup.
All files in
......\BMS\User\Config
axismapping.dat : Your controller mappings. Most likely to be reset by game
joystick.cal : keeps the joystick setting, AB, Idle etc.
dx9display.dsp : Keeps you screen res, and maybe some graphics settings.
phonebkn.ini : Keeps the list of your mp client/server connections.
Sometimes its a good idea, to just create an RAR (or ZIP) of the full BMS folder, and keep as a backup, if you can afford the space. (Current version zips to 900mb).