but I was afraid he might get bitten by the bat.
As long as the cat's had his rabies shot, I wouldn't worry about a bat bite any more than a mouse bite. The bat should worry about the cat, not vice versa.
I used to get one or more inside nearly every year. It was neat...I had cathedral ceilings throughout, with a 13 ft peak, and an open floor plan, with 35 ft. from one side to the other, over the kitchen and living/dining room. I'd just open the doors until it flew out, meanwhile admiring its flight skills, and ducking once in a while.
The cat was always interested, too, but he never scored.