Call your doctor's office and explain the situation and ask them if they will consider writing off or providing a discount for the bill. Although there is no legal requirement that the doctor advise you whether or not a particular lab will accept your insurance, many offices are concerned with patient satisfaction and will be willing to work with you to resolve this problem.
As the prior respondent indicated, call your doctor's office first. Explain your confusion of why you would be receiving a bill after they referred you to the site for service. Hopefully, you have evidence of their referral. Give them a chance to resolve the issue. If they are unable to resolve the issue, contact the site that drew the blood and ask them why they are not able to draw blood for the insurance you have. As a last resort, your insurance likely has a provision for covering expenses out of network. There is normally a large deductible associated with these expenses. Furthermore, your insurance provider should have some type of an appeal process that you should investigate.