How dangerous is a bee sting if you are not allergic?

Not very: Bee sting reactions are generally innocuous. They hurt and swell at the sting site but very rarely cause any other problems.

It is generally not : Too dangerous unless you are allergic or you have many stings. The greater the number of stings the more the venom load. My father once had over 200 stings from yellow jackets (which are wasps not bees). There was no doctor in our country (blue ridge mountains). He felt severely ill for over a week.