You can use $US anywhere in Belize, and interestingly, cannot leave the country without paying the exit tax ....in non Belizean currency
I suggest getting a good supply of $1 bills: the cab will be $25us plus a tip, and you will want another $1 at the water taxi, as its easier than trying to say you don't need help!
And for a final tip....if you change planes in DFW, hit TGI Fridays for a great cobb salad: It may be the last really fresh one you see 'till you get back, a week later and 10lbs heavier