No worries about rabies if your cat is vaccinated.
I think it'd be pretty cool to have a bat in the house. We've had plenty of birds, some brought in by the cats and some find their way in alone. I think a bat would go outside at night if you turned on every single light in the house and opened the doors to the darkness. Same with birds, only opposite. At aviaries, they keep the birds in open cages by using a "curtain of darkness". The birds rarely fly into where the humans are because it's dark in there.
I had a little squirrel in my empty pool the other day! Put the ladder back in and he high-tailed it out of there!
Karen
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insidious ungovernable cardboard