If you don't need to transfer a huge sum, a series of ATM withdrawals from your home checking or savings account on your debit card can work. I believe Atlantic Bank still allows a BZ$1000/US$500 daily limit, so in theory, if the ATM is working, in a week you could get BZ$7000. Both your home bank and the bank in Belize will charge a withdrawal fee plus an your home bank likely will charge an international transaction fee, and these fees add up.
--Lan Sluder