I grew up in Whitfield area of Bradenton, and live in south Sarasota now.
There's definitely not a whole lot between Alafia/Boyette and North Port Trails that I'm aware of that qualifies as "mountain biking" and not just "trail riding". There are flat bike trails at most of the state parks, and if you're in West Bradenton you might already know about the shell trails at Emerson Point Preserve
(you have to click through for Emerson... a direct link wouldn't work).
Garry, feel free to say "That's right" after this one too...