Can a provider bill the patient though he is contracted with local blue cross if patient has an out of state plan?

Providers who are not "in network" for the particular version of Blue Cross cannot be sure of being reimbursed for treatment they provide. Thus, they must bill the patient, who then takes on the responsibility of dealing with the insurance. Most providers will assist with this, if asked.

This is an issue with the insurance company, not with the provider.