the thing is, to me a doorbell is that box on your wall with all the chimes and whatnot in it, the doorbell switch that sits on your front door is just a dumb ole switch.
so if your just wanting to use that switch (and again its not a drastic amount of distance from there to where you want your arduino) you can just wire it up like a normal button example
if you want to tie into the actual doorbell, that requires voltage considerations and yadda yadda