I think the recent debacle in Indiana played a significant role in FL HB-583 and SB-1464 being dropped from the current FL Legislature sessions. Also a LOT of campaigning and petitioning in Tallahassee by LGBT activists. I'd bet the Bruce Jenner interview will be helpful also, as he it portrayed TG/TS in a positive way, and many people saw the "normal" human side of transgender people as compared to the side-show freak portrayals of the past like on the Jerry Springer show.
Most of these potty-panic bills are pointless, as protective statutes have long been on the books to discourage sexual predators from entering public restrooms inappropriately or with nefarious intent. Florida has a very strict and proactive sex-offender program, and registered sex-offenders here already know the rules and harsh penalties for violating 5hem. I think it's mostly political, the extreme right using scare tactics to build a voter base composed of religious extremists. I also think recent events have put these extremists into a minority of their own.