Hi, I always understood that a DC bell required an interruptor. eg a switch which breaks the current through the bell coil as soon it pulls in, same like a claxon in a car.
An AC bell has a coil which resonates on the frequency and operates the gong
Although I can't see why a DC bell wouldn't work on AC, as long as the voltage rating is the same, in principle it will work.
The product of rotation, excitation and flux produces electricty.