Kfander, how big was the bat that your cat caught ?
We used to see the bats flying around street lights at night, probably catching the plethora of night-bugs that were always swarming around the street lights. They were way too far up in the air for a cat to even think about catching though.
The bat that my friend had in the house had gotten in an open door or window, if I remember right; and she and the kids she was babysitting were all terrified by that poor little bat.
I am sure that he was as scared as Norma was, especially since she was after him with the broom.
I can't exactly remember how I caught him (her?); but I managed to do it without hurting the poor little fellow, and I am sure that he was glad to be turned loose again.
I did take him home first; but my mother was not keen on the idea of me having a bat for a house pet, so he had to join the goup flying around the streetlamps at night.