Falling off motorcycle

Very likely not. First, just to clarify--you never "go after" an insurance company; you need to sue the person him- or herself and then their insurance may step in to defend them and pay.

Second, the fact that you were hurt does not mean that someone needs to compensate you. For there to be compensation, there must be fault--either someone intentionally did something wrong, or someone was unreasonably careless (negligent). If you were test-riding a motorcycle, then unless the motorcycle was in dangernous disrepair and the lack of maintenance caused your fall, it's hard to see how what happened is the owner's fault. And no fault, no liabilty.

Check your own vehicle insurance policy--some may cover you for injuries which occur while borrowing or testing vehicles.

Although I do not practice law in the State of Florida, here are my initial impressions.  First, I do not completely agree with my colleague's advice.  It is possible that the owner of the motorcycle had an insurance policy that would cover riders that were using the bike with his permission.  I suggest that you consult with a local attorney to discuss this matter in greater detail to determine whether you may be able to be compensated for your injuries.  Good luck.