The best way to handle payment of medical bills is for the person obtaining the service to send the bill to the other person with an enclosure letter or email, keeping a copy. Unless otherwise specified in the Order, the courts will view thirty days as a reasonable time to reimburse. Extraordinary or non-emergency expenses or elective procedures should not be incurred without prior consultation with the other parent in order to avoid problems.
Failure to reimburse expenses can be enforced by a contempt action in court, but the Court will expect you to be able to prove that you gave the other person proper notice of the expense before filing the court action. Make documentation a habit and you may have smoother sailing with your ex-spouse, and will automatically have the proof you need for court.