I've always been scared of bees.
That's pretty common. Why are you afraid of them?
I am utterly terrified of the idea of being stung by bees.
Being stung is not a pleasant experience. There is nothing wrong with having a fear of being stung by a bee.
Does it not make me look bad to be afraid of a little insect?
There's nothing wrong with being afraid of a bee sting. Especially because you don't know how your body will react. The best you can do is avoid them and try to live your life.