Chris . . .
If we assume that this little bottle was made in the USA, fully mold-blown bottles weren't available till after the 1903 Owens machine was introduced. Owens machines left a valve mark on the bottom of the bottle. This bottle is fully mold-blown and has no valve mark. That leads me to conclude that this bottle is no earlier than say 1930.
That being said, I've had this nagging thought that the bottle may not be USA-made. The bottle was found on "a mangrove island in South Florida," which may or may not be in the Keys. (There are lots of other mangrove keys around the tip of the State.) Mangrove roots trap floating bottles, some of which are from foreign ships.
I have the impression that the mold used to produce this bottle was used long after a USA glassworks might have retired the mold . . . just my impression. But, if the bottle is foreign-made, it could be as recent as you suggest -- 1950 or thereabouts.