thanks @KatyJoy I would need a different surgeon tough because it's my surgeon who is charging the extra $8K over the scheduled fee. I was told that in the public system I would wait 12 months for an appointment then another 12 months for the procedure. I could ask my surgeon to recommend a surgeon who works public and see what she says. I can call her on Monday.
I also just found a form on the BUPA website that says
Members of private health insurers are not eligible for benefit payments for surgery or treatment considered to be cosmetic pursuant to the Private
Health Insurance Act.
But there is a form your specialist can complete to request surgery (special eligibility form) that perhaps allows your specialist to inform the health fund that it's required surgery. I'll explore that possibility as well.