How can Fla. Sheriff's Dept give a DUI to bicycle rider without probable cause?

You certainly can get a DUI on a bicycle in Florida. The public policy behind this law is that you may hurt yourself or cause a traffic accident by riding your bicycle while impaired.  The facts you have mentioned pertain to the basis for the traffic stop and not whether you were impaired. A police officer does not have to have probable cause to make a traffic stop, only a reasonable belief that you violated a traffic law. Once he is in contact with you if he has reason to believe you are impaired, such as smelling alcohol, then he has probable cause to begin a dui investigation.