The team on the BUPA helpline are pretty knowledgeable. I've just been through this process with them.
Sleeve gastrectomy is item 31575, comfirm that your insurance covers this surgery.
The private hospital cover network and member hospitals are listed on the BUPA website. You need to check where your preferred doctor operates. If it is one of the network or member hospitals you are in luck.
Your preferred surgeon will be able to give you a quote.
You need to ask if they participate in the no gap with BUPA, but most likely you won't be able to claim any of the costs back. If you have top level extras you may get some of your dietician costs back, you can log in to BUPA and check this online.
The quote should detail
the surgical assistant costs,
the anaethatist and
Some surgeons also require a psychologist assessment.
Once you decide to go ahead you pay the amount in your surgeons quote and book in to the private hospital. You will need to pay any hospital excess and copayment when you go in for admission.