In terms of billing depends how they got it structured. Usually the anaesthetist comes induces anaesthesia that would be one charge. The next would be the charge of the reversal of anaesthetics and the final would be the post -op 48 hour surveillence stand by they do. Depends how the hospital is structure if its their anaesthetist or another Dr, then the hospital will charge him for theatre time and equipment usage which the Dr will no doubt bill you for.
Too many variables and too little information supplied. The best thing is to phone the Dr and ask why if you really want to know but its pointless, you have to settle the difference.