And would they become zom-bees?

Honey bees die after stinging because they leave the stinger and venom sack behind. Essentially killing them because they lose part of their abdomen. Those types of bees RARELY IF EVER sting in self defense ONLY to protect the hive. You need not be scared of being stung by a honey bee when it’s away from the hive.

The sorts that sting in self defense are the ones that do not perish after stinging, like wasps and hornets. They do not lose their abdomen and therefore do not die and can sting as much as they like.

what about wasps

they can sting you multiple times without getting their lower abdomen ripped off so that's another story

due to the event of multiple wasp class breaches, full p a n i k has initiated.