I have had an American electrical/mechanical doorbell for years. It has two solenoids and the plungers strike a resonant bar of metal. It wasn't loud enough to be heard throughout my home. So i went to buy a better one and saw the same thing as I had. It was expensive.
I also saw a cheaper Chinese electrical/mechanical doorbell that has plastic resonant chambers beside the resonant metal bars and it works much better and is much louder.
Of course it is powered by a transformer. The transformer is cheap and is good quality.
It is not the place of discussing about countries. The point is that someone is going to make a battery powered doorbell,whatever the reason is. Is it obligatory to explain the reason of choosing the project? Remember we are here to assist not to disdain.
Use a Monostable timer made of 555, and drive base of a transitor with its ouput. Connect Collector of transistor with 3V and emitter with circuit. Connect the push button such that it triggers the 555 every time its is pressed.