You could try this. Put in:
Process the file once including the full bibliography. Then run bibtex. Now put in:
Run (pdf)latex again, and the bibliography will not be printed (merely treated as a "comment"). Unfortunately, you'll need to remove this (or comment this out) the next time, and then re-add it in alternation to keep things in order, but if you wait until you have your final document ready and then put it in, you should be OK.
This basic idea is stolen from this question.
(Somewhat unrelated, I find that I need to manually define
\newblock to get
natbib working with