Hi youngknapper,
I live in SW Fl. There are many woods that will make a bow in FL but the trick is, of course, finding it.
When I started, I fiddled with all kinds of stuff and had successes and failures. It was good for learning. My best advice would be to find a way to save some money and get a good Osage stave from a reputable source then honestly take your time and produce your best effort possible.
Possible FL bow woods? Cypress, Sea Grape, Mulberry. Pop Ash makes a very good bow, hard to locate. N FL will have possible oak, hickory, and other options. Buttonwood, fruit woods, bamboo. I believe black mangrove can be used. There really are lots of possibilities. Be aware of harvesting from protected areas.
If you are at ground level and just want to jump in you could fiddle with all kinds of stuff to gain experience but having a good seasoned worth while stave to invest your TIME into is worth a certain price.
PM me if I can be of further assistance.
Good luck!