I live in Bradenton, but I'm afraid there's basically nothing around here. I went to a place in Myakka off of SR-70 once, didn't know it was protected land when I went in (because I'm apparently blind or can't read) and then got stuck. Luckily, I knew a guy with a 4x4 F250 who came to pull me out before I got into trouble with the law.
Later, I found out about a mud hole off of Rye road that's privately owned, but open to the public (alot of local kids take their jacked-up trucks there), but it was more like a lake. I had a big Bronco at the time and it didn't stand a chance. Plus, the neighbors kept eye-balling me, so I left and haven't been back.
I agree with the above, Richloam, Croom, and Ocala are probably the closest, best places. If you want to pay there's Hard Rock MX Park (it has a Jeep trail) or Redneck Yacht Club (if you're in to mudding, though they apparently have four trails -- prolly for ATV's, though). There's also, apparently, a place in the Everglades called Big Cypress ORV which you get to along I-75, but it's, obviously, very swampy so you'd better be prepared to get wet. Maybe bring an air-boat along to pull you out, JK! If you find anything else, please post. I'm always keeping an eye out, but, unless you know someone with land around here, you tend to be SOL. Good luck!