A rabid bat is no longer a "bat" it's the rabies virus with wings. It will NOT behave like a healthy, or even typically sick bat.

There's two major presentations of rabies when it's in it's contagious stage, one is that the bat (or other animal) becomes "dumb" - it might just lie there, or maybe try to approach you if it's motor functions aren't completely compromised.

The second is the one you hear about more - the "angry" response. The motor function portion of the brain isn't as affected, but the part that creates the "fight or flight" response is, and the lever is stuck on "fight". It WILL attack anything it happens to get close enough to.

Regardless, the bat is no longer experiencing conscious thought. It's not a bat, it's rabies with wings.

You're far more likely to get bit by a dog or hit by a car.

This is true but has nothing to do with this discussion. You're probably also more likely do die by choking on a bat that accidentally flew into your mouth.