All surrogacy pregnancies should have a written agreement in place that spells out who will be responsible for payment for pregnancy care. Without such an agreement, problems will arise. If the surrogate has health insurance that covers pregnancy care without a surrogacy exclusion clause, you can bill her payer for the care. And yes, you would use o09.81_ for the supervision of pregnancy resulting from ART. There is an excludes 2 note regarding Z33.3 which means you can also bill that code if applicable. And of course you would also add the Z3A code for weeks gestation. If the surrogate does not have coverage for this type of pregnancy the agreement should spell out who pays the bills - it could be that you would be sending the request for payment to another party. But keep in mind that sharing of health info with someone other than the patient has to be guarded with permission in writing. So I hope your provider did not simply drop this in your lap. This is not your problem to solve and you need more information to bill correctly.
Thank you for the helpful information. Since my post, we have not had 4 additional surrogate patients and your advice has been helpful!