like a bat out of hell - Phrases/Idioms
The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 2003, 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Moving extremely fast, as in She ran down the street like a bat out of hell. This expression presumably alludes to the rapid darting movement of bats and, Charles Earle Funk theorized, their avoidance of such light as might be cast by the fires of hell. [c. 1900] For a synonym, see like greased lightning.