I've had to do this several times, it's really the best way to handle birds and bats that get into your home -- just toss the towel on top of it and pick it up. Another trick if a bird flies into your window and stuns itself, you can pick it up with a towel and place it in a (closed) cardboard box outside in the shade so they can recover without a ton of sensory input/stressors, you just have to make sure predators don't get into it.
(If you ever have to relocate a bat, don't just leave them on the ground, they can't take off from there and will almost certainly die. Put them in a tree or somewhere higher up)
As a PSA: if you’re in North America, do not handle bats. They are the primary rabies vector and due to their tiny sharp teeth, it is possible to be bitten unknowingly. Rabies is (almost) 100% fatal once you have symptoms. Leave it to the professionals who are vaccinated and know how to handle them safely. In the US, local animal control can usually help.