Bees do send signals to their companions through body movements, such as the location and distance of honey sources, but I have never heard of sending out "killing the enemy" signals.
Bees have barbed spines. After the stinging person or animal flies away, the barb will leave the sting mark in the skin of the person or animal, and part of the intestine will be involved. The bee can't live, and there's no way to move reinforcements.
As long as you are not standing near the "fried nest" hive, or there are no noisy bees nearby, you will be fine.
Are you sure it's a bee? If it's a wasp, it has no barb.