The only issue at hand in my mind is "were you at fault in this accident". The ticket for no insurance is BS, even if driving without insurance isn't the brightest of moves.
Realistically speaking, I think they're going to sue you for the $13K. Realistically speaking, I think the civil court will find the fact that you drive without insurance (when the state mandates it) to be acceptable proof that you're a negligent driver. I'm not saying it's RIGHT, but I'm saying it's likely to happen.
You should prepare for being sued. If you have some form of proof (photographs, eye witness statements, documented statements from the biker) that the accident was not your fault, make sure you can provide them in court. And again, prepare to be railroaded and found liable for the accident.