So you want to use this output to control the Arduino instead? First I figured it's the other way around.
Should work.
Connect the GND of Arduino to the GND of your door bell, 3V should be high enough even on a 5V system to detect as HIGH when you digitalRead() the pin. Otherwise you can always use an analogRead() and see if the value is high enough (should be about 600 for 3V).
please post code between code </> tages, so it looks like this.
Scanning your code I see you have some debounce in it - why? It's not a button.