To check out a contractor, there are several ways. For those who want to do it yourself, go to
DBPR Professions - Construction Industry Licensing Board which is the web site of the Florida Department of Business and Professional Regulation. They are the ones who license contractors. There is a link there titled "Verify A License" - use it.
Almost for certain, a new shower would require a building permit because of the plumbing issues - you would need a licensed plumber. If it is only a re-tile of an existing shower, maybe not because that depends on several variables.
The best place to visit is Seniors Vs Crime. They can check out the contractor for you, help verify the license, look over your contract, help you set up a payment schedule to avoid ripoffs, etc., all at no cost to you. They have two offices in TV - one in the Marion County Sheriffs Office at Buena Vista and CR 42 (352-753-7775) and one in the Sumter County Sheriffs Office at Morse and CR 466 (352-489-4600, Extension 4606).