Bermuda, like Dave's triangle shows, isn't in the Caribbean, but much, much further north.
A bit of background info on the West Indies Federation from Wikipedia:
Provinces
The provinces of the West Indies Federation were:
* Antigua and Barbuda
* Barbados
* Dominica
* Grenada
* Jamaica (to which were attached the Cayman Islands and Turks and Caicos Islands as dependencies)
* Montserrat
* Saint Christopher-Nevis-Anguilla (present day Saint Kitts and Nevis and Anguilla)
* Saint Lucia
* Saint Vincent and the Grenadines
* Trinidad and Tobago
History
The Federation was an internally self-governing, federal state made up of ten provinces (in the British West Indies), all British colonial possessions. The federation was created by the United Kingdom in 1958 as a way of simultaneously satisfying the demands for independence of all colonies in the region. The legal basis for the federation was the British Caribbean Federation Act 1956, and the date of January 3, 1958 was set by an Order-in-Council proclaimed in 1957.
The head of state was Queen Elizabeth II. Her Governor-General was Patrick Buchan-Hepburn, 1st Baron Hailes.
The combined population of the West Indies Federation was between 6 and 7 million people. The proposed site for the capital city was Chaguaramas, a few miles west of Port-of-Spain, Trinidad and Tobago, but the site was part of a United States naval base.
The Federation maintained a particularly close relationship with the nation of Canada, which had a similar past of being a part of the British Empire and becoming a Confederation. In the early years several Caribbean leaders suggested the West Indies Federation should investigate the possibility of joining the Canadian Federation but this was never more than a fleeting interest.
This did not stop Canada from providing the West Indies Federation with two of the region's most important gifts, these gifts were two merchant ships named "The Federal Palm" and "The Federal Maple", these two vessels visited every island in the federation twice monthly.
Although the Federation was initially optimistically embraced, the unity did not last. The largest provinces, especially Jamaica and Trinidad, quickly gained control over the federal government's agenda, much to the displeasure of the smaller provinces, and were reluctant to establish a customs union. This in turn caused the larger provinces to resent being members of a union that had so many members hostile to them, and increased pro-independence sentiment. Federal elections were held on March 25, 1958. Two Federal parties were organised as confederations of local political parties, both of whom were organised by Jamaican politicians; the West Indian Federation Labour Party by Norman Manley and the Democratic Labour Party by Alexander Bustamante. The WIFLP won the election and Grantley Adams (of Barbados) became Prime Minister.
Dissolution
In 1961, the Jamaican province held a referendum on political secession from the Federation. It passed, with 54% of the vote, despite the opposition of Manley, the province's Premier at the time, and Jamaica became a fully independent country. After Jamaica left, the next largest province, Trinidad and Tobago, left in 1962, (the Premier of the time, Eric Williams saying "One from ten leaves nought" ("zero"), and after the departure of Trinidad and Tobago, the country was soon wound up.
The situation was regularised by the Parliament of the United Kingdom's West Indies Act 1962. The remaining provinces reverted to being colonies supervised directly from London, most of which became independent later on, as follows -
* Antigua and Barbuda - 1981
* Barbados - 1966
* Dominica - 1978
* Grenada - 1974
* Saint Kitts and Nevis - 1983
* Saint Lucia - 1979
* St Vincent and the Grenadines - 1979
Anguilla, the Cayman Islands, Montserrat, Turks and Caicos Islands remain overseas territories of the United Kingdom.