The first time was in 2002 at Camp Lejeune, NC, when a red wasp ended up going down the collar of my jacket and t-shirt. It stung me several times before I got pulled over and out of the gear and un-tucked my shirt. The next time was in 2011 in Wisconsin. I was wearing an open-face helmet as I was only riding in a village with a top speed of 35 mph, so I figured "why not?". A honey bee hit me on the side of my chin, leaving its stinger in my face. Both of those incidents were more annoying and amusing than painful.
Far worse than those two incidents was hitting and being sprayed by a skunk. Instant, uncontrollable gagging, involuntary closing of the eyes. Lucky to be on a Ural because I think if I were on a two-wheeled bike for that incident, I'd have gone down.
Last summer, I had the worst incident. I rode from New Braunfels to the Canyon Lake dam when I suddenly started feeling a bug crawling up my sleeve. I figured if it was a stinging bug, that it would have stung me already. I could feel the tickle of it crawling across my skin as it went up my arm to my back. I could feel it crawling on me all the way back home and figured it was probably a june bug as it wasn't stinging and it was evening time and they were out in large numbers. Only after I was in my neighborhood, about a mile from the house, when the thing decided to identify itself with a sting to the middle of my back. It felt as though I were being branded. The worst sting I've ever felt. Worse than any bee, wasp, scorpion, or spider I'd ever felt before. I rode like Evel Knieval to my house, jumped off the bike, and then slammed my back against the wall of my house in order to kill the unfriendly, unwelcome passenger. I then ripped my gear off to find that it was a hornet. The pain of the initial sting only got worse as the evening progressed. By morning time, my whole torso was in pain and my breathing was difficult. It required a trip to the emergency room. I was given a shot of some sort of antihistamine and spent the next day in bed. It took a few days for the pain of the sting to die down. It kept me from sleeping, it was so bad. This past July, I had a slightly milder reaction to being stung on the thumb by a paper wasp as I was mowing my lawn. I guess our body chemistry changes over time, as I have obviously developed an allergy to wasp and hornet stings. Now, when stung, my plan is to head immediately to the closest emergency room.
So, as long as you're not allergic, bees and wasps are only a nuisance. Far worse is being sprayed by a skunk. But if you ever develop the allergy, it's a real nightmare.