Allergies to bee stings are actually a fairly common problem. However, the severity of the allergies varies quite a bit: some people have minor allergies that they don't even notice and some people have life threatening allergies. If you are concerned for a specific reason, I would recommend talking to your primary care doctor
An allergic response occurs when a foreign substance (in this case the bee's sting) causes the body's immune system (specifically cells known as mast cells) to "over-react" and release substances (namely histamine) that causes an inflammatory response. The severity of the response can vary. At a minor level, there is minimal itching and redness around the area -- pretty much everyone has this. At the worst -- the entire body release histamine and there is a body-wide response. This can become very dangerous if the inflammation causes swelling in the upper airway and therefore the airway closes off and the person cannot breath. This is the somewhat rare version that can be fatal.
Normally, people develop an exaggerated response that is severe after the immune system has already seen the foreign substance once. Therefore it would be unusual to have a severe reaction to the first bee sting.
Talk to your doctor for more information. Testing can be done beforehand if desired, although this is rarely helpful. I think insect repellant is probably your best bet! Good luck!