There is a season on Bobcats. Otherwise, unless you can articulate how the cat created a well rounded reasonable fear of immediate injury or death from attack... messing with it is a no-no. FWC will not respond nor will they try to trap the cat. Same with bears... FWC is fucking useless when it comes to these things INCLUDING alligators. FWC will only send a trapper, who can take up to two hours to respond, for gators over 4' in length.
I think bobcat season starts Dec 1 and runs to March 30th or close to those dates... you will need to double check this.
Bobcat (D)(F)
Statewide
Dec. 1 - March 31 by all legal rifles, shotguns, muzzleloaders, crossbows, bows and pistols
Those with a hunting license may possess no more than 1 bobcat and 1 otter pelt between April 1 and Nov. 30, 2013, unless pelt has FWC tag. Also, otter and bobcat pelts may not be taken out of Florida unless tagged. Bobcats may be chased with dogs year-round.
Bobcat: No Limits