That just seems like a lot of unnecessary work - the door bell pushbutton is a simple normally open switch - disconnect it from the AC and wire it directly between a GPIO pin and ground.
Or just rectify the switched 12v ac, filter it a bit, (you don't want the cap too big or it won't turn off), turn an optocoupler on with it, & use the output transistor of that device to switch 3.3v to the PIC, or whatever.
It's not as if it has to be a fast detection of the switch function.
Another way, if you can get at the transformer, is to rectify & properly filter the 12v ac prior to the switch.