Cat attacks Bat?

I've read that many vets believe that if they have ever been given the rabies shot they are unlikely to contract it again, however it's not something you want to risk. Symptoms aren't generally obvious until after a few days. I doubt it's rabies but there are a ton of other diseases that the bat could be carrying so it's best to get things checked out. Also it's important to note that rabies is also super dangerous for humans, so be careful.

Take your cat to the vet. Bats don't often have rabies but they frequently carry the rabies virus and can infect animals they might bite. If your cat contracts rabies, it will be a few days before they start exhibiting odd behavior. Your vet will know what to do. This soon, it is possible that she can be given the rabies shot now, but your vet might recommend that you quarantine her for 14 days. Just because you didn't find a bite doesn't mean that the bat didn't break skin.

She needs to go to the vet and needs to go now. Bats are a carrier of rabies. This means they have it and are not sick. Bats are this way with tons of different diseases. Your cat, and the bat, both need to go to the vet.