Not to sure if they have laundry facility's there, they might. If not there are a few places on the Caye that offer Laundry Services at a reasonable rate within walking distance. Someone will gladly point them out to you when you arrive as everyone on the Caye is very friendly.
Try Marie Laundrymat on middle street by the bakery. She charges buy the pound and is reasonable. Just drop it off and she can usuall have it ready in a couple of hours and it's clean and smells GREAT.