@helensimp
Ah... if you want to do it remotely, it's certainly possible, but trickier...
(a) You will need someone (an attorney or trusted friend) who can liaise with the notary to get the appropriate notary deed drawn up, and go to the notary on your behalf to sign it for the sale. You might also want a preliminary contract (with a sizable deposit) instead of going directly to the notary/notary deed step. This would be an attorney task, rather than a notary task.
(b) For them to sign for you, they will need the correct power of attorney document (probably one drawn up by a Bulgarian attorney), and it will need to be signed by you and appropriately certified. You can do this at the Bulgarian Embassy in London. Or you can notarize it at your nearest UK notary BUT then you have to send it to the UK Legalization Office in London who will legalize it for use abroad.
(c) You will need to consider the issue of the payment for your apartment. If the buyer will transfer directly to your account, then no problem. But it's a different story if they expect to bring cash to the notary, or pay after signing, or pay your representative. Or pay by cheque. :-)
In light of the above, if the attorney is charging 800 euros to draw up the POA, the preliminary contract (if you want one), check the notary deed, and go to the notary for you, it's probably in the ballpark. And you definitely need someone. And you can weigh this against the cost of flying over to sign.
I've done a remote purchase, as the process is much the same. However, for a sale, I think you have to be much more careful. The issue is the verification of the notary deed (that you're selling to the true buyer at the true price, and not to my mate Vasil for 1,000 euros), and the handling of the money... and making sure it ends up in the right place (your account).
So it might be less stressful to fly over and be here to sign (even if you have an attorney helping you).
Or, you make sure (even if you pay more) that you get a highly reputable and trustworthy attorney, rather than choosing Google first's or cheapest pick. There are many folks that I'd trust to sign a document for me at the notary... but the list gets a lot shorter if they're leaving the notary with 150k euros! :-) I have an excellent attorney in Plovdiv (who's registered with the Bar Association, and I'm happy to provide his details) who has helped me (and many other expat.com members) with a number of issues. He could certainly act for you, but I'd guess that he would charge at least 1,000 euros, plus expenses for someone to go to the Burgas notary. And, even though he has been very reliable over the last 5 years, I have not put 150k euros in his bank account... and I would still prefer to avoid doing that if I could! :-) So I would definitely ask him if there's a way for him to draw up the preliminary contract to make sure you have all the purchase funds in your own bank account before he signs the notary deed to complete the sale.
Alternatively, I have used BulgarianProperties.com several times, and they are a very large and reputable agent with listings all over Bulgaria... and a focus on overseas marketing to find expat buyers (typically means better prices). So if you don't have the buyer yet, they could find the buyer (for a commission)... and I'd be pretty confident in giving them my POA to deal with the sale.
In the above, I've assumed you have a Bulgarian bank account to receive the funds. Not sure how easy it will be if you only have a UK account now. And there's the issue of getting it out of Bulgaria after the sale (easy if you have online banking, but if not you'll probably need to make a trip here anyway).