I've never seen a tornado while on a bike, but I got caught in a severe thunderstorm (in flat rural farming area) with hail bouncing off my helmet. I made it to the next small town and took shelter at a restaurant. There was a tornado nearby, but I didn't know that until later.

I've seen one tornado, but it was a tiny, pathetic thing. I was driving when I saw it. I was glad to be about 1000 feet away though.