Please see our article on immersion in natural bodies of water for more information.
We also recommend checking the website of the local Chabad center, http://www.jewishvirginislands.com/. Look under “Tourist Info” and then under “Mikvah.” Currently, the site indicates that there is no official mikvah on the island; however, it gives a phone number for the Chabad rebbetzin. We suggest you make this contact, since she most likely has experience helping tourists with immersion in St Thomas.
B’hatzlacha, and enjoy your vacation!