Since Brexit, getting residence is more challenging as we are now non-EU citizens.
There are several grounds for granting a D visa. So, for example, if you are a student, or a retiree (with proof of pension) it's pretty easy. Otherwise, not so much.
So what are the alternatives to struggling for the D visa?
DELAY the D visa
You can still buy property in Bulgaria, and visit visa-free for 90 in 180 days. You may be able to wait a few years until you qualify for your pension. If that's too far away, you could establish a UK (or other location) company and do some minimal trading for 2 years. This qualifies you to register a TRO (Trade Representative Office), which will also get you the D visa. The level of trading isn't very important, it just needs a minimum amount of history, and be in "good standing" with all taxes and corporate fees paid up to date. The UK is quite inexpensive for incorporation and ongoing fees, so this doesn't require a huge investment.
GET (BREXIT - Article 50) Residence instead
There is still a lot of confusion about this. Some EU countries had fixed deadlines in relation to Brexit and granting residence. But most (including Bulgaria, Cyprus, Spain) don't.
This means if you were in Bulgaria in 2018/2019 (pre-Covid) and you already purchased property here, then you can claim residence rights under the Withdrawal Agreement.
From what I've read here on the forum, there are many Brits in this situation who were prevented by the Covid Crisis, and resulting travel restrictions, from getting over here in 2020/2021. Hence they missed the chance to submit their application during the Transition Period. And, unfortunately, most of them believe (incorrectly) that they have therefore "missed the boat".
Obviously, this doesn't apply if you've never been to Bulgaria, and you're just fed up of the D visa process. :-)
GO somewhere else
This is pretty frustrating if you have your heart set on Bulgaria. I enjoy my life here, and I always recommend it highly. But sometimes you gotta just pick your battles. :-)
My favourite alternative recommendations are:
(a) Serbia. It's our Balkan neighbour with similar climate, culture, food, property prices and cost of living. However, much easier for non-EU citizens to get residence. Here, you don't need a long-term visa first, you can go there and apply directly for residence (like Bulgaria pre-Brexit). It will be granted if you purchase a Serbian property (I don't think a minimum price is specified, or it's quite low), or you incorporate a Serbian company (along with corporate bank account with some funding).
The Serbian option gives you residence in the Balkans, and it's an easy drive to Bulgaria. The Serbian company as well as getting your residence there, should also qualify you for a Bulgarian TRO after you've had it for 2 years.
(b) Spain. It's always a popular destination with Brits. I'm always shocked that Bulgaria doesn't allow the same visa basis as Spain, but they don't. Spain has the "no lucrativa" visa, if you are not yet retired, but are of "independent means". You can't work with this visa, but you can live in Spain indefinitely. For this option, you need income of almost 2,500 euros per month (or show savings of 30,000 euros which demonstrates that income for a full year).
That sounds like a lot, but if you sell a house in the UK you will have more than that. Use those funds to get the visa/residence. After it's granted, the funds are not tied up so you can then go buy a property.
The Spanish options gets you residence in an EU country. After 5 years, you qualify for permanent residence. This is almost as good as an EU passport, and lets you live, study, work, or retire in any EU country (including Bulgaria) on the same basis as EU citizens (i.e. it's a formality, just need to show proof of residence in the new country, proof of funds, and proof of health coverage).
(c) Turkey. It's our Mediterranean neighbour, also popular with Brits (and many others). Hot and sunny like Spain and Bulgaria. Similar cost of living to Bulgaria. Nicer sea/beaches than Bulgaria's Black Sea coast. This has a similar requirement to the Spanish no lucrativa visa where you can show savings/income to cover your new life there. (But much less than Spain, as you only need 500 euros/month income, or 6,000 euros in savings.)