What you are trying to do it fairly easy to accomplish. I would suggest you either use Processing or Perl (my favorite) on your mini to monitor the serial port where the Arduino is plugged in. Then just come up with a scheme such as send the letter "A" when the doorbell is rung. From the Processing or Perl side it is simple to then read that "A" and trigger your applescript.
Check out:
http://arduino.cc/playground/Interfacing/Processing
http://arduino.cc/playground/Interfacing/PERL
To trigger an AppleScript from the command line, use osascript: Documentation Archive
The reason I mentioned Processing is that if you are a little familiar with Arduino, then Processing is pretty simple to pick up.