No reason you couldn't. Remember - bcp runs from a command prompt, so you can "parameterize" that any way you wish. If you were to enclose that in a CMD file (which we call runme.cmd), using very rough syntax like this
set dirpath=c:\myoutputdirectory\myfilename
Bcp [various BCP options] %dirpath%%1%.csv
You could run runme 20071004, and it would create c:\myoutputdirectory\myfilename20071004.csv from the output of the BCP.
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Your lack of planning does not constitute an emergency on my part...unless you're my manager...or a director and above...or a really loud-spoken end-user..All right - what was my emergency again?