my question is whether one can use a Bulgarian-issued Maestro debit card on ATMs or in supermarkets in Bratislava? I know some countries prefer Visa over Maestro, that's why I ask.
You should have not problems with with withdrawals from any ATM marked with Cirrus sign - and I didn't met European ATM without that sign (for some reason ATMs don't use Maestro sign directly).
Yes, in some places you may have problems with using Maestro or MasterCard to pay directly. But supermarkets shouldn't be among them - this problem applies rather to smaller shops or restaurants.
Assuming your bank allows foreign transactions on that card, it would certainly work in Bratislava. Most ATMs there support Maestro card withdrawals and Slovakian banks issue Maestro cards.