Bat out of Hell was a common rural expression in the southeast US a half century ago. Meatloaf originated the expression in 1976 or thereabouts with the mid-70s Zeitgeist eponymous album "Bat Out of Hell." The expression 'like a bat out of hell' has been in common UK-English usage for decades meaning to fly, usually figuratively. Bats have been associated with witches and the occult, and therefore thought to originate in the bowels of hell, as they fly quickly as if in panic, to make the comparison with a bat flying out of hell for anything going recklessly fast would seem quite natural and likely to be a country idiom prior to being recorded in print.
Look at this maniac driving behind me!! He's coming at us like a bat out of Hell.