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.
American Heritage Idioms
Phrase(s): like a bat out of hell
Inf. very fast or sudden. (Use caution with hell.) • The cat took off like a bat out of hell. • The car pulled away from the curb like a bat out of hell.
McGrawhill's American Idioms And Phrasal Verbs