If I am injured while riding my bicycle in Florida, can I sue the driver that hit me?

You can sue the driver that hit you while riding a bike as long as the other driver was at fault. In other words, there has to be something negligent in the way the driver operated his vehicle to cause the accident, but in that case, assuming there is negligence and the driver of the car was at fault, then you can make a full claim for all the damages you suffered due to your injuries from being hit by that car.