It doesn't matter if you use USD or BZD currency to any vendor here. They will give you change at a 2/1 basis. As for how much cash you should have, that really depends on your individual needs and what you will need to pay cash for during your first few days if you can't get cash easily from a cash machine. How much will transportation be to your accommodation and, afterwards, to any place you might wish to visit? Are you going to want to shop at any small street stands or food vendors? Do you need to pay in cash for any part of your accommodation? I'd consider having as much cash on you and available as you'd have at home for a week if you're absolutely confident your debit card will be accepted here.
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