What to do with a stunned bird in your home?

Hello everyone. My neighbor has a cat who sometimes brings home birds that she has hunted. I am called upon to help with removal.

This morning, the cat brought in not a dead bird, but a completely stunned bird that seemed otherwise uninjured. The bird was standing and rocking back and forth slightly because it was breathing hard (I think).

I was not sure what to do in this situation. I read online to make holes in a paper bag, line it with a cloth, and allow the bird to rest in there in quiet for 1-2 hours, so I did this.

Was this the right thing? Does anybody have any other suggestions? The bird is currently rehabilitating in the house next door as I write this.

Thank you in advance for any suggestions. I want the bird to be OK, and don’t want to put it outside until it can fly.