The bank is listed as an international bank on the Central Bank of Belize's website. It's a real bank (formerly called British Caribbean Bank International Ltd.) and, as far as I know, they accept foreign companies.
Banks in Belize aren't very picky. You will find that most so-called International Banks in Belize open accounts for almost anyone who can fill in their application forms.
They have email addresses under "Other Contact Options". Have you tried one of those?
10 days is extremely long to wait for a reply. I wouldn't wait more than a few days before moving on. Heritage Bank and Choice Bank usually respond the same day or at latest the next day.