How should I deal with the motorists insurance company?
In Florida, if you're a cyclist involved in an accident with a motor vehicle it's basically a good idea not to deal with the other side's insurance company as far as giving them any statements. Often times insurance companies attempt to talk injured cyclists or injured motorists into statements.
By law in Florida due to the rules of contract, you're only required to give statements to your own insurance company. You are absolutely not required to give statements to the adverse party's insurance company. It's always a good idea when those circumstances arise and you're involved in an accident, the other side's insurance company is trying to contact you, it's a good idea to hire an experienced personal injury attorney so they can prepare you to speak with the other side's insurance company.