Hi Claude - I have a condition that causes postural pain (while lying down) but have had 3 hysteroscopies, none of which made any difference to the pain. I had one under GA, one under local & one with no anaesthetic or sedation whatsoever. It is over very quickly - the last one for which I was fully conscious, only took around 5 mins, including biopsy.
I would explain your concerns to them & see what they say, but I would urge you to go ahead - it's important to have unexplained bleeding checked out, though almost always nothing to worry about. You could ring the dept beforehand & explain the nature of your back condition so that if they advise cancelling, the appointment slot can be allocated to someone else. They should be able to arrange for you to have pain relief if the GA is not enough to prevent this occurring afterwards. I hope all goes well.