Bahamas World built up a fleet of three used 707s in 1972-74, when they all were repossessed. After a while they seemed to make a comeback from 1976-82 with odd leased Convair 880, 707 and DC8 capacity, generally just one at a time and sometimes none, seemingly from the nearby Miami grey-market community.
International Air Bahama (later just plain Air Bahamas) seems to have been a much better funded operation, with a long-term relationship with Loftleidir in Iceland, and behind them Seaboard from the USA, whose DC8-63 aircraft they leased long term. They built up to a near-daily Nassau to Luxembourg (where they touched the Loftleidir operation) low-fare scheduled service, nothing else really, selling on bus connections to Frankfurt and Paris etc. They operated from 1968 to 1981, for the first year with a 707. There are a number of (inevitably simplistic) timetables here.
Air Bahama