BERMUDA
Bermuda was almost captured twice during the Revolution:
1.
http://www.redcoat.me.uk/bermuda.htm <--Details both the 1777
USS Randolph attempt to take the island and the more detailed 1779 attempt stopped by
HMS Delaware. By ten freaking minutes!

2.
http://www.rootsweb.ancestry.com/~bmuwgw/ships7.htm <--Confirms the
Randolph as being at Bermuda in June 1777 specifically.
3.
http://www.carolana.com/SC/Revolution/sc_troops_militia_outside_sc.html <--Confirms the 'two brigs' noted in the first link as being at Castle Harbor and thus gives the specific date of the
Randolph/the two brigs as being at 13 JUN 1777.
4.
http://books.google.com/books?id=ZI...nepage&q=Had the Continental Congress&f=false <--Notes that Bermuda had sympathies enough to America that had the Continental Congress 'possessed a fleet' that could've held Bermuda, the colony might be lost to England.
5.
http://books.google.com/books?id=Iu...&resnum=1&ved=0CBYQ6AEwAA#v=onepage&q&f=false <--Bermudians actually sent delegates to the Continental Congress.
Bermuda in general was sympathetic to Americans both on principle (it was the second-oldest British colony and an official offshoot of Virginia), and for pragmatism - it gave gunpowder to Washington in the infamous 1775 'gunpowder plot' and was the ONLY British territory America traded officially with during the war; Bermuda needing food as badly as America needed Bermudian salt. Generally, had the Americans JUST been lucky to hold on in 1777 or get there ten minutes faster in 1779, the colony would've been in a desperate enough position to give in and join up.
BAHAMAS
IGNORE THE 1776 RAID. That was ALWAYS meant to be just a raid and nothing more. However, the Americans were generally thought to have been INVITED, which should give you some insight into the Patriot sympathies Bahamians held. Rather like Bermuda, the Bahamas had a 'ALMOST' in being captured in 1778. The following links explain:
1.
http://books.google.com/books?id=UG...ult#v=onepage&q=Battle of Nassau 1782&f=false <--LT Rathburn occupies Nassau again in 1778. Had he ambushed
HMS Gayton successfully he likely would have held the island chain, as the islands were not valuable enough for warships to cruise around and protect compared to Jamaica or the Leeward Islands. Indeed, the Spanish expedition (readable as you go down) captured the isles without a fight...then a Loyalist expedition (further down, again) did the same in 1782!
2.
http://www.hazegray.org/danfs/escorts/de1057.htm <--gives the specific date of Rathburn's occupation as 27 JAN 1778 and more details on his occupation.
3.
http://books.google.com/books?id=ud...#v=onepage&q=Bahamas American culture&f=false <--More details on the American occupations. Also details how America and the Bahamas continued to share culture and blood both before, during, and most importantly well after the ARW.
4.
http://books.google.com/books?id=M5...&ct=result#v=onepage&q=Gillon Bahamas&f=false <--Information on the 1782 Spanish capture. Actually, note how 'without American help, there would have been no attack on the Bahamas.'
5.
http://books.google.com/books?id=Iu...&resnum=1&ved=0CBYQ6AEwAA#v=onepage&q&f=false <--Same link as Bermuda #5, but note:
the Bahamians may have invited the 1776 raid themselves. If that doesn't spell 'pro-American', I don't know what does.
The Bahamas, like Bermuda, were an official offshoot of a mainland colony (South Carolina) and in this case also were sympathetic to American concerns both princpled and pragmatic. They also were similar to Bermuda in that they only truly became important AFTER the Revolution concluded; with massive population increase and new strategic interest. Again, had the
Gayton not been warned in time Rathburn likely could've held Nassau for good.
Ironically, the Loyalists were still American and on both island chains demanded and got the Lord Proprieters kicked out (in the Bahamas) and more powerful legistative assemblies produced, rather like how New Brunswick was split off for Loyalist demands.