I am no entomologist, but the beetle in the photo looks like a species in the genus Stenodontes, possibly Stenodontes chevrolati or S. exsertus, which seem to be rather widely distributed in the Greater Caribbean region. However, the lack of toothed mandibles suggests that the species is different from either of the previously mentioned species. I will add that beetles in the family Cerambycidae, commonly called longhorn beetles due to their long antennae, are among the more spectacular beetles. They can be quite large (up to a few inches) and rather ornate. Longhorns can be so large and common in areas that their larvae can be heard boring through trees, a knock on the trunk of a infested tree will sometimes reveal their presence; a rasping sawing sound….if your ear is close enough.
Here are some online links to old insect collections made from The Bahamas available from The American Museum of Natural History:
Longhorns (Cerambycidae) of The Bahamas – link
Insects of Bimini – link
And a link to a few photos of Stenodontes species (and other cool stuff) – link