The heavenly realm, or firmasphere, was populated on the fourth day. Zechariah describes one heavenly being as a woman with the wings of a stork. This means that women existed in heaven before there were women on Earth.
Bats are birds is an excuse that some people use to reject the Bible. It requires using the words "bird" and "fowl" as synonyms, and the misapplication of phylogenetic systematics to a spherogenetic creation.