Since it is a British owned country, I would assume you need the JAA stuff. I'll check around. What kind of airplane? N registered or Bermuda?
It sounds like you need a Bermuda pilot license Validation to fly Bermuda registered AC.
http://www.dca.gov.bm/Registration/HowToRegister.aspx
In order to use the JAA system the country has to be part of JAA, the only country or territory that is currently a member but lays outisde the geographic Europe is Turkey.
Some countries may be using the system of a JAA member, for example France, all the former French Colonies and Territories use the French licensing system and the airplanes are reg "F" but you can`t use any JAA license, just a French issued CPL or ATPL, which is based on the syllabus they had way before JAA. It`s a ridiculus system, for example I know some pilots in Brazil that hold an ATPL of a JAA member country like Portugal, but they are not allowed to fly on any other airplane reg in an other JAA member state, if they want to they have to do a conversion...
Most former British and Dutch colonies actually use regs based on templates the FAA (CARS) made so that many of this countries could meet higher standards, this was really important in the Central and South American region so that many carriers would be allowed to fly into the US. India uses many things based on the JAA, but it may be the only one out there.
