I would look for oilcloth or maybe even a laminated cotton.
These can be tricky to sew with so I would invest in a
Teflon foot which allows the sticky cloth slide under your pressure foot without getting stuck. These feet are relatively inexpensive and would be worth the investment.
Here is a pattern that features some "wet" pockets:
http://annamariahorner.blogspot.com/2009/02/multi-tasking-naturally.html The pattern doesn't state that there are specifically pockets for holding wet items, but there's a few photos of the same bag with pockets made from laminated cotton. In fact, the easiest would be to find a bag pattern you like and simply use laminated cotton or oilcloth for the pockets.