My M.O.
Use the plastic grocery bags obtained when provisioning take a few ashore every time and find a trash can. If that's inconvenient, or you can't find trash cans, just have everyone grab a bag or two when you're somewhere you can pay to dispose of larger quantities.

Also, if you're chartering out of the USVI you're supposed to dispose of any "international" trash (open things that can spoil) before coming back. It's ridiculous. However, we do it. I give our left overs to the nice kid that works at the ferry dock in Great Harbor, JVD and then dump as much trash as I want in the nearby dumpster.