Make sure that your bank in America can do an ACH Transfer.
It takes a few days to "Test" the bank for reliability (they make two small deposits, and you need to confirm them)
Use Only your BB account number, and just monitor your account with their on-line service. once verified, a transfer can be set up as one time, or you can make it repetative.
The transfer takes 3-4 Business days, and once completed, you need only use your BB ATM, to access your funds.
(I would recommend updating your passbook, for showing to immigration if and when they ask.
It IS NOT an international Transfer. Bangkok Bank of New York is an American Registered Bank.