In Florida there are ordinarily no restrictions regarding the purchase or sale of a firearm to a private individual so long as neither the seller, or the purchaser are "prohibited persons". No bill of sale is required, although that is sometimes a good idea for both individuals - and could be as simple as a signed handwritten document describing the make, model, serial number, name of purchaser, name of seller, and date of sale. Again - not necessary - just sometimes a good idea. Purchaser must be a least 18 years of age, and you should make sure the purchaser lives in the State of Florida by checking a driver's license or other official photo i/d. Likewise the seller should be at least 18 years of age, or the sale could be declared invalid. You have no responsibility as a seller to ask the purchaser if he or she is a "prohibited person" or if he or she has a felony convictions, etc. - however, if the purchaser tells you they do, and you still sell it - you've committed a federal felony.
Nick