Whilst this is technically possible, it is not an ideal process.
The only way Medicare allows this is for you to process the Medicare claim as an unpaid patient rebate. In these situations, Medicare generates a cheque in your name, which they send to the patient. The patient then needs to bring the cheque to you so you can cash it at the bank.
Medicare's preference is for the patient to pay the full amount upfront and then receive the rebate, which results in the same out-of-pocket expense for the patient as if they were paying only the gap.