If bats had the same migration pattern as birds, I would say that it would be a real concern. But I don't think bats migrate, so the chance of an Asian bat infecting an American bat is pretty low. I also do not think there is enough interaction between humans and bats in most countries for the bats to catch Covid-19 from humans. At least, I'm assuming that most people avoid bats. Although there could be some very strange people out there who seek interaction with them.
When I was a young caver it seemed to me that bats tended to colonize one cave as a species. Mexican Freetails is what you have in the Southwest. I don’t think other species “roost” or whatever the term is in the same caves.