If you're trying to cool the source, then the denser the fluid the better. A vacuum is the worst (radiation only), and a liquid is the best, right?
But if you're trying to heat the bottle, then a denser (higher pressure) fluid might slow that process down by absorbing heat itself.
Finally, I...
A good and inexpensive source of properties, including compressed water, is NIST's REFPROP:
http://www.nist.gov/data/nist23.htm
I did a quick check and it looks like about 1% increase in density for water between atmospheric pressure and critical pressure at about 80F.
Above critical...