@berryd
As @GB_2_BG writes, you need a notary in Ruse to execute the sale/transfer of the property.
And, further, as @GB_2_BG also writes, you don't need to be present at the notary, you can execute a POA (Power of Attorney) to allow someone present in Bulgaria to sign on your behalf. There are Bulgarian Embassies in both UK and Cyprus, who can witness/notarize your signature. A POA executed at a Bulgarian Embassy is ready for use at a Bulgarian notary, and does not need further legalization or translation.
However... while I'm not an expert on remote transactions... I think it's significantly more complicated than presented by @GB_2_BG.
NOTARY
Firstly, I think it's unlikely the Ruse notary will be OK with an English conversation with an British seller, so there is a potential language (and translation) issue. Secondly, I think the notary is an independent party, so can verify/allow the use of the POA, but can't be the one you delegate to (so you need a trusted third-party - maybe two, as there is both a buyer and a seller - who will go to the notary, with the POA, and sign). Thirdly, I think the notary will draw up the Notary Act (in Bulgarian), but I don't believe they will draft a legal document like a POA (somebody else has to do it). In other words, you probably need to insert a Bulgarian attorney (I can recommend a very good one, with excellent English) into the mix, as they can liaise with both buyer/seller, and deal with the notary and Notary Act, and draft suitable POAs for both buyer and seller, and go the notary (or nominate their usual gofer). If the seller is not happy with one attorney acting for both sides (it's certainly not recommended by purists), you'll need two attorneys. :-)
To give a similar example, I'm currently buying a property in Bansko, which I'm purchasing via a large property agent. It's a large company, so they have an in-house attorney. He deals with the notary and Notary Act documentation, and prepares the POAs. Because it's a large and reputable agent, both the seller, and I (as the purchaser), are nominating the same person (one of the company's employees) to act as directed by the in-house attorney, and sign for both of us at the notary.
COMPANY
While you purchased in your personal name, I don't think you can ignore the company issue as you're selling a house. You don't say who's buying the property, but as they're in UK, I'm guessing they're British. If they are British they will need to purchase via a Bulgarian company. (If they are EU citizens, or UK citizens with Bulgarian permanent residence, this won't apply, and they, like you, can purchase in their own name.)
I don't think the notary will get involved with company creation issues, so, again, this means you need a Bulgarian attorney in the mix. And a different set of legal documents as you need to incorporate a Bulgarian company, open a Bulgarian company bank account. And you need a different POA.
I'd say there was significant buyer risk in this aspect, so you need to ensure you have a reputable attorney involved.
MONEY
The big issue with remote transactions is not the POA (this is just paperwork), but handling the money.
The buyer needs to give someone the money, and they need to have high confidence that this someone will take it to the notary to buy the property (and will make sure the property is assigned to the buyer, not to themselves or their best mate).
The seller, similarly, should be receiving a (huge, hopefully) sum of money for selling the property. Again, you need a trusted party in the mix to ensure the funds go to the right place.
If the notary will accept an international transfer from the buyer in the UK, and make an international transfer to the seller in Cyprus, then perhaps it's the notary handling this issue. Or perhaps it's another reason for having an attorney involved.