As far as I know, this expression means to appear suddenly and in a scary way. But what is its origin? I heard that it comes from Meat Loaf's song but I'd like to confirm it with reliable sources, if possible.
The OED has this phrase meaning to "(to go) very quickly" from 1921:
1921 J. Dos Passos Three Soldiers (1922) ii. ii. 67 We went like a bat out of hell along a good state road.
However, I found some antedatings.
First, from August 17, 1895 in the Evening Star (Washington DC, Page 15, Image 15), in an article titled "COWBOYS AT WORK / Hamlin Harland Gives His Impression of a Round-Up. / THE CRUELTY OF BRANDING / Some Stirring Encounters Between Man and Beast. / WITH THE COW BOSS":
The branding was soon over and then the camp began to move. The next round up lay over a formidable ridge, and as I rode behind the troupe with the boss, I saw a characteristic scene. Toiling up the terrible grade, one horse on the cook's wagon gave out, and four of the cowboys hitched their lariats to the pole and jerked the wagon up the gulch "like a bat out o' hell," as one man graphically put it. In this way do these men dominate all conditions.
Placing the quotation on the map, the report itself is from "SALEDA, August 4, 1895" and begins "At Cripple Creek mining camp...". There's both a Salida (note spelling) and Cripple Creek in the state of Colorado, just 50 miles from each other as the bat flies.
Next, two antedatings via the American Dialect Society mailing list. From Stephen Goranson:
The Lions of the Lord: A Tale of the Old West By Harry Leon Wilson, Copyright 1903, published June, 1903, page 107 (google book full view):
Why, I tell you, young man, if I knew any places where the pinches was at, you'd see me comin' the other way like a bat out of hell.
From Fred Shapiro:
1906 The Cosmopolitan May [article beginning on page 81] (American Periodical Series) A peon shot back the bolt of the bull-pen door and in poured the bull like a bat out of hell.
Finally, Dialect Notes (Volume III, Part V, 1909) is good as it gives a descriptive reason for the phrase:
Actually, it means to run away from something with great speed and recklessness. Searching for the etymology of this expression has lead me back to the late 19th century/early 20th century and appears in the southern US states initially.
An early book on dialect, called Dialect Notes, Volume 5, 1918, issued by the American Dialect Society, includes the phrase, its meaning and locale:
I was surprised that there are no biblical references (that I could find) to this expression.
"Swiftly" is the word used in most historical references I found online. The notion of wrecklessness has been implied in my own experience hearing and using the expression.
This concept is mentioned in the comedy play The Birds (Greek: Ὄρνιθες Ornithes) by Aristophanes, first performed in 414 BC. Chaerephon, a loyal disciple of Socrates, is a bat from hell in this play (lines 1296 and 1564):
CHORUS "Near by the land of the Sciapodes there is a marsh, from the borders whereof the odious 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 Ulysses, stepped one pace backwards. Then that bat of a Chaerephon came up from hell to drink the camel's blood. " http://www.classicreader.com/book/1801/6/.
More info about the play here: http://ancienthistory.about.com/library/bl/bl_text_aristophanesbirds.htm