BFE is an abbreviation for "Bum Fuck Egypt" or "Butt Fuck Egypt," which is used to denote "out in the middle of nowhere."
I'm curious how this expression came about. UrbanDictionary.com has a user-submitted definition with the following etymology:
As I understand (and other people have corroborated), it derives its existence from another expression “bumble fuck” (I am unsure if it's one word or two), both of which mean "out in the middle of nowhere." I am fairly certain that the inaccurate “butt fuck Egypt” derived from bum being the English term for buttocks. Clearly the definition of BFE is the same regardless of what one believes the “B” stands for, but I thought is was worth correcting.
I have no idea how accurate or reliable the above etymology is. There is no entry on EtymOnline.com.
Best Answer
Summary
Bumfuck, Egypt is first documented in army slang from 1972, and BFE is from at least 1988. Bumfuck, [Egypt] appears to be the original, followed by variations Bumblefuck (1989), Bubblefuck (1993) and Buttfuck (1999).
Sometimes these variations appear standing alone, sometimes in Egypt, or Africa (also found in BFA), or another country, (rural) state or place, and sometimes prefixed by East or West. More recently, both BFN and Butt Fucking Nowhere are reported from 2002.
As Bumfuck, Egypt appears to be originally military slang, given the number of abbreviations they used I can easily believe it was also jocularly and euphemistically shortened to BFA before 1988.
Partridge
The Concise New Partridge Dictionary of Slang and Uncoventional English (2003):
It also gives BFN and Butt Fucking Nowhere, both from 2002.
OUP
These 1989 and 1972 first citations are given with others in The F-Word (2009, Oxford University Press):
It also gives Bumblefuck as a 1989 alteration of Bumfuck; Bubblefuck as a 1993 alteration of Bumblefuck; and Buttfuck, usually used with a placename, from 1999.
Usenet
I found an earlier example for the initials BFE in Usenet, on 11th September 1988 in alt.cyberpunk: