1) Appeal to your insurance company. Pretty much all carriers have written appeal methods. Explain that you chose a network physician and a network facility and that no choice was available to you for the Anesthesiologist.

2) Make small payments along the way. Send $25 or $50 each month to keep them off your back and to keep them from sending this to collections. Appeals usually take 30-90 days. If the bill goes to collections, your options are much more limited.