Actually, I think it would be the moose that was hitting the bicycle.

No, I've never been run over by a moose.
I did run over a deer once. It was lying dead on the edge of the road. It was dark, and I was kind of not paying attention. It's a mostly deserted road. I think I hit the neck. Otherwise, I might have gone flying if I had hit the larger body section.
A deer ran across the road in front of me a couple weeks ago. Kind of freaked me out. Just like I had seen them do with cars. Zing, out of the ditch and across the road about 15 feet in front of me.