This may be an answer to Derek's comment rather than to Andrew's original question.
They are commonly written on walls right in front of an elevator, stairs, or an escalator, or on elevator buttons. They stand for Basement 2nd Floor, Basement 1st Floor, 1st Floor, 2nd Floor, as Andrew wrote. In Japanese, when words are abbreviated, they are usually abbreviated in romanization or abbreviated after its English word. Writing
F would require much less strokes than
I did not know that they are wasei-eigo. Are they not used in English? Or, do you mean that the word order
Basement 2nd Floor is wrong as English and should rather be
2nd Basement Floor or
2nd Floor Underground or something? If you mean that, then it might be wasei-eigo. The idea is something like 'negative 2nd floor'.