you will prob need to call a limo/cab service. I don't remember there being a shuttle service. I used to always rent a car at RSW and drop it the next day at the Naples airport as it was the cheapest option.
here is a link to rental places
try going to Mousesavers.com to look up any discount rates you can apply for pickup at RSW.
Maybe this will work depending on where in Naples you are heading. If N Naples it may not be much of a savings
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