using AC power for piezo buzzer

No, I didnt miss it.

I have to disagree, for 2 reasons.

We dont know exactly what the OP is doing. This buzzer may well be run via a separate doorbell switch from the main electromechanical bell. If so, the buzer, being relatively low consumption, will see more or less unloaded voltage, ie well above 12.8.
If the buzzer is parallelled with the existing doorbell, again we dont know what the bell design is. Last electromechanical one I had used a mercury switch and a solenoid to bang back and forth between 2 ding-bars. This means the current draw was being switched on-off-on-off while in use. So again the buzzer is liable to see unloaded transformer voltage.

So I think we really can not assume either way, and need to design soemthing that will work either way.

again I'll disagree. V will rise high when the load isnt drawing its max current, or close. Without knowing the buzzer circuit, we dont know either way. It may well consist of 2 current drawing parts, the oscillator and the oputput device, wit no inbuilt supply line cap. If so, the osc will likely draw current while the output device is in its frequent off states. If so, feeding the buzzer from an R will give it a chopped supply, 23v or similar and 12v. This could cause problems.

Yes, one can, just that a single resistor is a far more elegant solution imho than adding a series of parts, maybe including active etc. A zener would add continuous power consumption too, it works but not the best.

looks a lot neater to me :) What can I say. Its all calculable, but I wouldnt attempt to, trial and tweak is far quicker. My initial guess would be 1/4 the R required if the R were after the reservoir cap. That should be somewhat on the high R side for safety.

I have in pervious posts, assuming 33% transformer regulation. The devil is in the differing assumptions. Yours may work as you say, but I think its taking chances.

To be precise, I conveniently ignored the chocke rectifier option, since thats not likely here. That would give a lower reservoir voltage.

You could ask :-). If it wasn't clear from my previous posts, I intend to take power right off the contacts of the solenoid of the existing bell.

I'll try to describe the existing setup. The bell has two chimes, and they are metal bars, each about an inch by half a foot. The solenoid is spring loaded. When the button is pressed, the solenoid is energized, moving the plunger and causing it to compress the spring and strike one chime. When the button is released, the spring pushes the plunger back toward its rest position so as to strike the other chime. Of course the power is from a transformer, and the switch simply completes the circuit through the solenoid. As I mentioned before, I measure a steady 12.8 VAC across the solenoid when it is energized (ie, during the time between the two stikes of the chimes).