There is very little information about "surety bonds". Officially, it looks like FL is one of the states that accepts surety bonds as an alternative to liability insurance. What are pros and cons vs buying auto insurance?
It's a way to self-insure. You make a deposit to the State DMV or purchase a surety bond from a broker. The bond pays up to a pre-determined amount (usually a minimum of $30-50k) once you are no longer able to pay.
The upside for most individuals is that it is cheaper -- if you don't get into an accident. Also, I believe that the underwriting requirements are less strenuous -- the broker wants to know about your ability to pay. The downside is that you have more exposure to loss.
IMO, it makes more sense for a business that has a fleet of vehicles than an individual.