Bridger's Island is a private location somewhere in the Caribbean inhabited by Nathan Bridger.
Following his son's and wife's deaths, he inhabited the island pursuing his various researches, including hand signal communication with dolphins. During that time, he discovers Darwin in a nearby lagoon, cut-up by a fisherman's net, and nurses him back to health.
At the behest of Admiral William Noyce, Commander Williams leads an ashore team, having found the reclusive Bridger (DSV: "To Be or Not to Be").
The island still exists into 2032 CE, when Nathan Bridger brings his grandson, Michael Bridger, to the remains of the house (2032: "Brave New World").