It takes time to set up the wire transfer between U.S. accounts. I just had to do this and it took about 3 days working days. Once the transfer is set up it will only take 1 day after this for me to do it.
You can go to Atlantic Bank and send up to $499 U.S. (without a Central Bank permit) thru Western Union, but you must be using cash or credit card to draw on. The fees are pretty steep, you'll end up paying about 15% to do this, but the Western Union goes thru immediately. Moneygram is only available thru Belize Bank and we don't have one of those here on Caye Caulker. If you are going to send thru Western Union, do it in the morning as soon as the bank opens. Belize (the entire country) is only allowed a certain dollar amount each day by law.
Since you have a U.S. debit/credit card try going to the westernunion.com website and see if you can do it online.