You are not allowed to work, even in your own business, until you become a resident, or get a work permit. The Belizean government is supportive of foreigners buying or opening businesses because they expect they will hire and train locals.
Meet with a Belizean attorney who can advise you on this matter. It isn’t always cut and dry. And if there are other employees working at the business it may be possible to facilitate a work permit that will suffice until you get your residency, if you are the owner. Once you have lived in Belize a year, then you can apply for residency. But it takes a while to get your residency once you submit it.
There may be a work around on this. But before investing in a business, it will be well worth the money to pay an expert to help you, preferably a Belizean lawyer who specializes in this type of permit.