Many women (and men) travel alone in Belize. It seems like there are fewer singles in San Pedro than elsewhere in Belize but I could be wrong about that. You should have few or no problems. You will not have to deal with the machismo so prevalent in Latin America. Just use common sense and routine traveler's precautions. In Belize City, you may be hassled a bit if you go about on your own, or even in groups, but elsewhere no problem.