@Cheryl
I've rarely seen either private healthcare policies or public healthcare that covers much in the way of preventative care. The focus is almost always on remedial care when you're sick or injured. For example, the UK's NHS idea of preventative care is a cursory "Health Check" with the nurse at your local surgery every few years (5?). Bulgaria is no different.
In any case, the best preventative care is not obtained from any doctor! It's by you deciding to invest time and effort to improve your diet/lifestyle and level of activity, and hence be more proactive about your own health and well being.
Bulgaria's low cost and wide open spaces is great for a more active life. I do daily brisk Nordic Walking around my local parks (free), and I swim several times a week (about 5 leva per entry with a monthly ticket). I also do bike rides (free) up Youth Hill and a bit of SUP on the Regatta lake (free). I mostly do strength exercises in the park on my daily walk (free), but I also go to the gym occasionally (5 leva, single entry at my local ratty gym, 15 leva at the fancy new one).
My top recommendation for any new expat in Bulgaria is, if possible, to get enrolled in the public healthcare system (NHIF). We pay 40 leva per month as unemployed (you can also pay more as an employee or as self-employed). This gets you free or nearly-free public healthcare (equivalent to the NHS). If you're retired from the EU or UK, then you can bring your S1 which gets you full cover (once you've registered it with the health authority, and got yourself a GP).
One of the great aspects of the Bulgarian system is that most private hospitals are affiliated with the public system, and reimbursed by it. Hence, you can get VIP private hospital treatment, with little or no waiting, for a very small private surcharge. I have not seen another EU country that works the same way. Instead, most work like the UK, where you can wait in line for a few months for a free NHS op... or you can immediately get a private op at your nearest BUPA hospital, but pay the full private fees.
It took my old dad a couple of years to work through the NHS system to his hip replacement (but it was free). A UK private hospital probably charges GBP 15k-20k these days, but you'd get the op immediately. A Bulgarian public hip is also free, but perhaps with less delay than in the NHS. A private hospital (such as Tokuda in Sofia) perhaps charges around 15k euros, but this drops to around 1k if you have full public cover. Which, undoubtedly, is rather a bargain, especially as you can get it whenever you want it.
I routinely use my local private hospitals (Pulmed and Medline in Plovdiv, or Tokuda in Sofia if I need a bigger hospital with more departments) for preventative care. Usually, this means paying the full private fee (regardless of my public cover), but they are usually incredibly good value. Typically, around 100-150 leva for a consultation with the appropriate surgeon/specialist. Most tests/scans are cheap too, unless you want MRIs.
I've had consults (and relevant tests/scans) with a cardiologist, dermatologist, and orthopedic surgeon. But you can easily find a good gynecologist, gastroenterologist, endocrinologist, or whoever else you feel you need.
Some of the private hospitals here do offer a comprehensive health check package, but that might be quite expensive (guesstimate 500-1000 leva). A cardiovascular stress test (max HR, max VO2) is probably in the same cost ballpark. But I doubt most folks want to bother (especially as a cardiologist consult with physical exam/discussion + EKG + echocardiogram is around 150-200 leva).
I am registered with a local GP (under the public system, but he's based at a private hospital), and he can help with vaccinations if I want one. The local health authority deals with Covid boosters, and they'll also give you the annual flu jab (if you go buy one at the local pharmacy). The Covid booster is free, the flu jab is about 20 leva.
My main preventative care is a comprehensive blood test at Ramus Labs, maybe once or twice a year. The Ramus Mega has most of the important ones (including cholesterol panel and urine test) for about 25 euros. I usually pay about 70 euros, but add a bunch of hormone levels and cancer markers. This is much more comprehensive than anything you'd get on the NHS. I always do a fasting blood test, and go at 8 (when they open) so that I can get home for my big brekkie. The results are online a few hours later.
I also use the Pulmed emergency room (as it's next door to our apartment) as my quick and dirty way to check on any concern. For example, earlier this week, I did a faceplant off my escooter while buzzing through the woods as a shortcut to get home. It was extremely painful, but I was 90% sure I was OK. To be 100% sure, I popped over to the emergency room. The doc confirmed just bad bruising, no fractured ribs, and gave me a prescription for an anti-inflammatory. He also sent me for a quick facial x-ray to check I hadn't fractured my nose/forehead, but that was clear too. 15 mins wait to see the doc, 10 mins examinations, 15 mins to get the x-ray. Cost 160 leva (full private cost, inc. x-ray). That's pretty cheap... until you compare with going to the GP next day (5 leva consult, 5 leva for x-ray).
Separately, the other key preventative care is to make regular visits to your dentist and optician/ophthalmologist. I don't think Bulgaria's remedial care is generous in these areas, so definitely preventative care is all on us. I have a fab dentist here (probably the best I've had anywhere) and I visit twice yearly for check-up and cleaning. Ultrasonic toothbrushes are very cheap these days, so that's an easy, but very effective change. My dentist charges 150 leva, which is excellent value. My optician charged 50 leva a couple of years ago, but there is a very fancy new dedicated eye hospital (Luxor) nearby, and they charge in the 100-200 leva range.