The chances of being stung by a bee are very low, but I can imagine that the low hum of any insect can be fearful.
Will My Neighbour’s Honey Bees Sting My Kids? provides good advice about the chances of getting stung and how to avoid it.
I got stung once. When I was 5 or so I smashed a rock on a bee that was on a clover flower. I picked the rock up and the half-dead bee managed to sting me on my thumb. It was a good learning lesson, although it didn’t instill any fear of bees – more respect than anything.