John,
ASA offers a range of courses from ASA 101 (Basic Keelboat), 103 (Coastal Cruising); to 104 (Bareboat Cruising). Each one costs a few hundred $$; so your investment in lessons could be well over $1,000 b/f you ever board a charter boat. IMHO, it's not a necessity for chartering. My wife and I have done a fair amount of bare-boat chartering including in the Caribbean, Australia, Florida, California, Washington, and British Columbia. An important factor is boat ownership; if you own a 25-ft boat that you sail regularly; say monthly, that's a BIG plus toward getting a charter approved. I believe that a company would not hesitate much to bare-boat charter to you a 35 or 36-ft, perhaps larger, sailboat on that basis. A boating "safety" certificate that you can get on-line, sometimes at no cost, can be added to your resume; it carries some weight b/c that's what the insurance people want to see.
In a few places you might be given a written "Dock Master's Test" but this is not common and typically, in my experience, has been associated with charter companies that also offer, or arrange for, ASA courses. Go to a straight charter company (no school) and you might not have to take such a test. (They're a bit difficult to pass w/o much study unless you are already quite familiar with ColRegs, marine sanitation laws, and the names of the parts of boats and their hardware/equipment.) Field tests are also more characteristic of charter companies that offer instruction. However, the ones I've done were simple; tack, jibe, man-overboard routine, & engine use; but-- MOST importantly to the charter company it seems--docking skills. They want to be confident that you can return the boat into its slip, or pull up to a long dock, w/o damaging the boat. If you're not immediately good at it they'll keep walking you through until satisfied that you can do it well enough.
I don't think you'll find much interest in folks renting their personal boat to you. Too many potential liability issues, etc. But, if you wish to try chartering somewhere along the eastern Gulf coast look at St. Petersburg, FL. (As recommended above.) I have to tell you, however; in the summer (July, August, September) it's hot and muggy; not particularly the best time for even sitting at a dock unless the boat has AC; and then, you're just down below hiding out from the heat w/ the family. You may as well be in a hotel room that you could get for the same daily rate as you'll be wanting to visit the showers at least once a day! In summer, consider Anacortes in Washington state; several charter companies there--lots of boats. Good place to hide out from the summer heat of the Gulf coast!!! (But the down-side of that is FLYING!!)