Dear Gillian & Paul...
The UK is no longer a member of the EU, so getting residence is a little trickier than before.
So...
(a) Perhaps you don't need a residence permit? I believe UK citizens can stay in Bulgaria for up to 3 months in any 6 months, without any visa or residence permit. You can buy a Health Insurance for Foreigners policy here for less than 100 euros. If you're still living/working in UK, and you just want to enjoy the summer here, for example, this might be fine.
(b) If you want to live here most/all the time, then you do need a residence permit, and the first step is to apply for a D Visa. Then once you have that you can apply for the residence permit. (Visa can be applied for at any Embassy/Country, but residence can only be applied for here in Bulgaria.) This process is much easier if you are retirees with a pension (this is one of the grounds for granting the D Visa). Otherwise, it's tricky again... and I think the usual option is to go for Foreign Trade Representative.
(c) I think this is a real long-shot, but if you're feeling lucky, it might be worth a try. If you you own a property already, and have done so for a few years (so you have evidence of having lived here for some time)... and you arrive in BG soon (March/April/May)... you might be able to go to immigration and try to charm them into giving you a residence permit per the UK Withdrawal Agreement (up to 31/12/2020) on the basis of Covid making travel almost impossible, so you weren't able to get here in time.
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Here's some official info, I've copied:
RESIDENCE PERMIT FOR FOREIGN (NON-EU) NATIONALS
All foreign nationals who would like to obtain Bulgarian residence must first apply for a long-term D visa in the nearest Bulgarian embassy or general consulate. There are 5 primary instances for which a D visa is granted:
1. Registration of a Trade Representative Office of a foreign company in Bulgaria;
2. Registration of a Bulgarian limited company employing at least 10 local citizens for no fewer than 6 months;
3. Investment in real-estate property – 312,000 €; You may learn more how to buy a real-estate in Bulgaria;
4. Non-EU citizens who are pensioners and have sufficient funds & accommodation to support their stay in Bulgaria;
5. Family reunification in Bulgaria;
6. Bulgarian residence for European citizens;
7. Bulgarian passport by investment.
Our experience shows that the most convenient and affordable way for a foreign national to obtain a Bulgarian D visa and Bulgarian residence permit is by way of registering a foreign company’s trade representative office in Bulgaria. Registering a trade representative office with our law firm, we will not charge you maintenance or annual fees for the registered office address of your trade representative office.
FOR RETIREES
Non-EU citizens who are retired in their home country can apply for a Bulgarian Pensioner D visa and temporary residence permit. The required documents are published in Art. 24, sec. 11, para. 10 of the Foreigners in the Republic of Bulgaria Act.
Documents required for a non-EU Pensioner to obtain a long-term Pensioner D visa:
- Standard Visa Application form
- Two passport-size photographs
- Passport
- Document, showing that they are entitled to a retirement income, issued by the country of origin and legalised with a notary public
- Document from a bank in Bulgaria certifying that the applicant has a valid bank account to which regular transfers of his/her pension will be made
- Evidence of accommodation and address in Bulgaria
- Medical Insurance
- Police clearance certificate/ CBR check
The set of documents for a long-term Pensioner D visa is submitted in person in the nearest Bulgarian embassy or consulate. After the Pensioner D visa is approved, the foreign national can apply for a residence permit. The residence permit for retired people is granted for a period of up to 12 months and it can be renewed annually.