To move extremely fast, without thought, or in a panic. A similar phrase would be “like greased lightning.”
“Bat out of hell” was a common rural expression in the Southeast US a half century ago. Meatloaf commemorated the expression in 1976 or thereabouts with the mid-70s classic rock album “Bat Out of Hell.”
The phrase can be traced back to the Greek playwright Aristophanes’ 414 BCE work titled The Birds. In it is what is believed to be the first reference to a bat out of hell:
Near by the land of the Sciapodes there is a marsh, from the borders whereof the unwashed Socrates evokes the souls of men. Pisander came one day to see his soul, which he had left there when still alive. He offered a little victim, a camel, slit his throat and, following the example of Odysseus, stepped one pace backwards. Then that bat of a Chaerephon came up from hell to drink the camel’s blood.
In modern days we can visualize the rapid darting movement of bats and, as Charles Earle Funk theorized, their avoidance of such light as might be cast by the fires of hell.
The expression ‘like a bat out of hell’ has been in common UK usage for decades meaning to fly, usually figuratively. For hundreds of years, bats have been associated with witches and the occult — and therefore thought to originate in the bowels of hell. It may have been a country idiom prior to being recorded in print.
The expression first appeared in print in the US in 1921 in the novel The Three Soldiers by John Dos Passos. “We went like a bat out of hell along a good state road.”