Corporate medical insurance varies, depending how much each company wants to pay for the cover - some cover pre-existing conditions, some don't, so you need to call BUPA to find out. The Acute / Chronic thing is a very complex issue, and has resulted in a fair few court cases where insurers have been sued for denying cover. As a rule, things like MS, ME, ongoing depression are not covered but they generally pay for initial investigations, diagnosis and then issue a notice of withdrawal of benefits, which then means that condition is excluded. IME, it is very unlikely that any gynae issue is defined as chronic at this point, especially if a hysterectomy is a cure.
Nearly all policies carry an excess, you usually only pay once, but if your treatment spans a renewal date, you may need to pay twice, depending how the policy is set up.
Some medical insurers (and quite probably BUPA) have a list of preferred hospitals, where they have negotiated set fees for your stay. If they do have a list, you really need to try and get treated at one of their selected hospitals, as it can get expensive if you don't. They also have pre-negotiated fees for the surgeon and anaesthetist depending on the complexity of the operation, and the specialists know that they should bill within these limits.
I would also check if they are any limits on things like Out Patient investigations - most policies are unlimited, but there are a few where you get say £1,000 per year. Sounds like a lot, but have a few consultations, couple of scans and some blood tests and it quickly adds up.
BUPA do a pre-authorisation service, if you phone them prior to the consultation, they will be able to get a claim going, and get everything approved in advance. They will also arrange direct settlement with the hospital and specialists, so you won't be out of pocket at any point.
Finally, be aware that some costs are excluded - when I worked for a medical insurer, we didn't cover "Out-Patient drugs" - anything that was prescribed at consultation / discharge on private prescription, as it was considered that you could get these on the NHS. Also additional expenses at the hospital like telephone calls, internet access would be unlikely to be covered.