It seems you have no police report and no independent witnesses and you were making a left turn. So by these facts alone insurance companies will hold you liable. However the point of impact is in your favor. Let your insurance carrier handle it. If your injured, hire an attorney.
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Sounds like the facts of your case are in your favor, but that the insurance is giving you a hard time. I would get in touch with any of us on this chat. We all provide free consultations.
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If you have collision coverage, you can make a claim and it doesn't matter whose fault the accident is. If you don't have that coverage, you can sue the other guy in small claims court for the damage to your car. Keep in mind that, assuming he was hurt, he is probably going to sue you. Your insurance company will defend you and no doubt it will try to argue that he was partially at fault, no matter what they are saying to you now.
If you were hurt, a local PI attorney will probably take your case and help you sort all of these things out.
Problem here is you were bounded by a stop sign and the motorcyclist was not. You as the vehicle entering the roadway are under the duty to not enter until reasonably safe to do so. Speed on the other vehicle can be used to allege some contributory negligence on the motorcycle, but you will not escape the the underwriting assessment of 51% + fault.
You may want to contact your insurance carrier and clarify the situation to them to allow them to represent your best interests properly in your car accident case. Best of luck.