Most Health Funds these days have some sort of no-gap policy setup with some surgeons (I think!) I would go into a Bupa office and ask questions. I know funds have agreements with hospitals, dentists etc etc. I go to a dentist affiliated with my fund that has no out of pocket costs for checkups and cleaning and 70% rebate on basic dental.
They may have a list...I don't know but I have found if you get the right person to chat to you will often find helpful info re cutting costs.
I was lucky with my mastectomies in that my surgeon and plastic surgeon operated on me for a very small gap fee. My surgeon asked me what my health cover was. I was seeing him at one(big) hospital and he recommended another smaller private hospital that he operated at as he said there would be hardly any out of pocket expense. This was a long time ago before agreements between funds and hospitals. (at least I didn't know of any!)
I have just been on the Bupa site (which I'm sure you have!) and you can search fees, gaps etc if you haven't already.
http://www.bupa.com.au/find-a-provider As Judy said, there are often other bills that come trickling in unfortunately.
I am also in Melbourne.
Let us know how you get on. It will be of interest to others.
jezza
Dx Jan. 1992 9mm Grade 3 IDC node neg. LB mast. Prophylactic RB mast. 6 months later. No chemo. No rads. Saline implants. 22 years NED. (No Evidence of Disease)