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It would be better if the woman pays rent during her stay. Otherwise, it may appear that the real intention of the visit is that you both intend marry each other. If USCIS believes this to be true, then the visa will not be granted, and you will be advised to seek a K-2 fiance' visa, instead.
Having a lease agreement with the woman would help, as would her ability to prove sufficient assets or income to pay fair market rent for her stay.
In short, while the visitor must apply for the visa, your goal is to present yourself as an individual whose only interest is to rent a room to someone who you met on a visit to Jamaica.
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