Yes. You do have the right to sue or bring a lawsuit in a Florida bicycle accident. However, you don't have to proceed right to a lawsuit. If you've been injured in a bicycle accident, then you may have a right to bring a claim directly with the at-fault driver's insurance company and may possibly be able to negotiate a settlement without the need to sue. But, if you cannot come to terms, then you do have the right to sue or bring a lawsuit.