for you to try simply putting the buzzer on the output of an open-collector TTL driver, e.g. 7406 o4 7416. That shouldn't require a pullup resistor at all. It has the NPN transistor and the pullup on its base and can easily be driven by the port pin.

The primary thing is that the low-side driver works better with a limited supply voltage. I generally prefer low-side switching.

There are, BTW, mosfets, as Kai has suggested, with very low on-resistance, hence, very low voltage loss across them. They behave more or less as switchable resistances, hence, having a very low resistance, can allow a considerable amount of current to flow from a low-voltage supply.

RE