Not sure about Bermuda. Bahamas requires pet import, send money and form at least six weeks before departure, has an option for fax reply. Add VAT to cost. Need vet certification dated shortly before xing.
See noonsite and respective country's websites on pet importation.
there are many aboard with cats-- but the rules are a lil tight for bermuda and bahamas... noonsite has info, and more info can be found in a group on facebook named gatos del mar, specifically for cats at sea... https://www.facebook.com/groups/2777...?ref=bookmarks
For the Bahamas you will need to get there permit(from ag. Dept.) and health certificate. You will be required to have all the recent shot records and a vet. Certificate filled out right before departing the states.