I'm very surprised by such negative comments! I have spoken to a number of expats here who have had very good experiences with the Bulgarian health system. In particular, there is little or no waiting here if you want something done.
If you're resident, then it's pretty easy to contribute to the social security system here, and hence get free healthcare. I registered as unemployed and pay 13 euros per month (if you're proper retired you ask for an S1 from the UK and then it's free). And they gave me an EHIC for use in the rest of the EU. I think it's worthwhile to do this, just to keep your options open (and have no worries when travelling). I haven't even registered with a local GP, but that would be a sensible thing for you (and me) to do. There is an extra faff in trying to find an English-speaking one, which is harder in a tiny village than in a big city, but I'd say there are plenty around.
One very good aspect of the system is that private hospitals are fully integrated, and receive payment from the national health system. So you can go to a public hospital for free, or you can upgrade to a private hospital, and pay the difference between the state's payment and your VIP treatment.
I'm not sure I would do a major op at a public hospital here, but there are plenty of excellent private hospitals in Sofia, Plovdiv, Varna. I went up to Tokuda in Sofia (acibademcityclinic.bg/tokuda) for a consultation, and I was very impressed with the place.
Knee and hip and replacements are very common operations these days. Even if it hurts, you don't have to go direct to replacement, there are less invasive surgeries you can try first (various types of injections, or arthroscopic repairs/investigations). You can also try to defer by physiotherapy, low-impact activity (walking, pilates, etc.), supplements (chondroitin/glucosamine seem to have positive feedback), pain management (most effective is NSAID gels like Voltaren or Voltaren Max direct to the affected area), and mechanical aids (walking stick, or nordic walking poles).
Most of the private places can provide rehabilitation for a week or two afterwards, which might be a good idea. (It costs, of course.)
Turkey has a thriving medical tourism scene in Istanbul (and other cities) so it's definitely worth checking out. The cost is significantly less than a UK private hospital (and close by). But I think it's hard (but not impossible) to get the UK (or BG) healthcare system to contribute.
I found a very well-regarded clinic in Lithuania (nordorthopaedics.com) which is a specialist in knees and hips. The cost is highly competitive, so worth a look.
Toduka is pretty local (90 minutes from me), and will get the BG state payment. I think they will do a better class of op/prosthesis than NHS standard, with a private room, with extra rehab. Maybe at an extra cost of 1,000-2,000 euros. And you can get the op pretty much when you want.
You're in a different situation as you're still in the UK. If you move here, then I definitely recommend getting yourself into the local healthcare system, as I described. If your knee is very bad (and an op is fairly urgent), it's probably very sensible to stay there and go through the usual NHS process. It's a bit slow, but they do a good job. And your local GP will look after you, if there are any post-op issues. If it's something you're thinking about doing in the next few years, then it would seem better to move here as planned, and be in the system so that when you do decide you need it, it won't be an issue.