@Eddiey
Like @Vasilev, I also give Bulgaria "two thumbs up". :-)
He is an experienced immigration attorney and a long-term member here, who has helped many folks get through immigration formalities.
If you just want to check it out, you can stay visa-free (with UK passport) for 90 days in 180. But to stay longer, or study, you will need to get your residence permit.
For Brits (and all non-EU citizens) the process is D visa application in your local Bulgarian Embassy (London, probably)... followed by a residence application here in Bulgaria.
The commonest options for qualifying for D visa are pensioner (won't apply to you), or student (could be appropriate if you want to do a master's degree), or TRO (which might be an option if your parents' business is a UK limited company, more than 2 years old).
The TRO is a bit bureaucratic, with lots of paperwork, and an immigration attorney would definitely make it easier. But it's not cheap. Approximately, I'd guess around 1,000 euros for the first step, which is to get the TRO registered (based on your existing foreign company). Then maybe 500 euros or so to assist with preparing the D visa application paperwork. And maybe another 1,000 euros to then go to immigration with you in Bulgaria for your official biometric residence card. Maybe there's a "package" price, if you ask nicely. :-)
You need to check carefully exactly which documents can be accepted as is (e.g. your passport and passport copy) and which need legalisation/translation, because it's a costly step. Your Swansea degree certificate with "wet stamp" is your original. "Legalisation" is an official step for using a document abroad, which is done at the UK Legalisation Office (in London). Translation normally has to be done by a Bulgarian official translator (either here in Bulgaria, or, I think, at the Bulgarian Embassy).
https://www.gov.uk/get-document-legalised
My guess is that your main task is to get a Bulgarian university to accept you, and this is probably easy if you have a bachelor's degree, speak English, and have 4 grand for your fees. :-) There aren't very many options for degrees in English, so I don't think I'd worry too much whether it's a great uni. It's just a year's vacation in sunny Bulgaria. :-) Your university should have some guidance for applying for your D visa, once you have your official offer letter. There are loads of Brits studying near me at the Plovdiv Medical University, so it's nothing unusual. I don't know NBU, but they're legit and accredited, that's the main thing. I've heard that American University in Bulgaria (AUBG) is good, and has an EMBA (16k, which is a lot more than 4k, but not bad for an MBA). University of Economics, Varna has quite a few graduate options too, so worth a look.
https://www.linkedin.com/school/new-bulgarian-university/
https://www.aubg.edu/academics/executive-mba/
https://www.ue-varna.bg/en/p/8590/admission//master/master-programmes