Yes, they are out there! I've had two experiences with larger sharks there--at least, large enough for me. The first was several years ago when windsurfing from the Gulf back into the pass next to Caladesi Island. It was a really windy day and I had gone out on an old flat board. It was overpowered by the wind, and I had been catapulted more times than I cared already that day. Anyway, as I came into the pass and looked ahead, I saw a large shape in the water and thought, "Wow, I wonder what that is?!" My next thought, as I got a tad closer, was, "It's a shark!" It was, in retrospect, a funny incident. He (or she?) was about 5 ft long and passed DIRECTLY under my board as we were going opposite directions--he/she out to the Gulf, and me into the bay. Boy, did I ever balance carefully at that moment! And as I was sailing back to the causeway and fell a couple of times more, I can truthfully say that I was back on the board before getting wet! (Sailing over a shark on a windsurfer will do that to you...)
The second sighting--and a bit more bothersome--was just last month. I was sailing from the causeway to Caledesi Island on my Laser Zuma monohull w/ my children aboard and saw a large, brown fin cutting the water about 50 feet away. (I've seen lots of dolphins, of course, and this certainly wasn't one.) At any rate, I played it cool and didn't spook my kids, etc. I did tell them about it when we got home, however, and we did a little research on the matter. Turns out that tiger sharks have brown fins, and they happen to have the most deserved reputation for being not only man-biters but man-eaters. (!) They also grow to 21 ft... (Not saying this one was, but it was pretty large.)
Anyway, as I said at the start, they ARE out there, but you can't worry too much about it since their presence there isn't a new thing. Just be careful, and don't dangle any arms or legs in the water!!!
By the way, I've had a shark come to the surface within 10 feet of my old Sea Snark years ago in Clearwater Bay, and I've also seen several smaller, harmless sharks in the area (around 2 feet or so). Again, apparently they're a fact of life on the water.