@D H16
Congrats on the early retirement, and the great pension!
Certainly, when it triples you can live it up a little. :-)
You should bear in the mind that the legal minimum wage is around 400 euros per month, and many Bulgarian retirees might have even smaller pensions. So if you have nearly 4X this number (and later 12X) you are doing very well, comparatively. It should be absolutely no problem to get your D visa with this kind of pension.
Certainly, folks manage on far less than you, and you too could definitely manage. But with renting, and wanting to be in Sofia (the most expensive city) you probably need to be a bit more frugal.
I like BulgarianProperties (dot com) and I have used them several times. It's a very large and reputable agent, and they have listings (for sale and rent) all over Bulgaria. They work with lots of expats and have English listings and English-speaking agents. They can also deal remotely if you want to rent a place based on their listing, rather than making a trip over just for this. (You should note your D visa application needs your proof of address and proof of health insurance, not just your proof of pension.) Even if you don't want to rent through them, it's a great way to do a bit of research on what's available for your budget.
Sofia is the capital, but I would also consider Plovdiv (2nd city, and former European Capital of Culture), and Varna/Burgas on the Black Sea. But for frequent flying Sofia airport will be the easiest (lots of low cost flights from Wizzair and Ryanair), which means I'd stick with Sofia or Plovdiv. We live in Plovdiv, and we love it. I get Wizzair to Spain, UK, Cyprus, Greece and more. We get a limo service (90 minutes door to door) for 70 euros (or I drive up and park near the airport if it's a short trip).
I think a modern, nicely furnished apartment is now around 400-500 euros for a studio, and more for a 1 bed. I have friends who rented a very nice 1 bedroom apartment in central Plovdiv and that's 700 euros per month (so Sofia would be more, of course). And if you want one that will accept pets that will restrict your options, and cost more. If you want a nice 1 bed in downtown Sofia, that's pet-friendly, I suspect this could easily blow a huge hole in your budget! :-)