If I may bravely share my thought as a double-foreigner (not a Bulgarian and not even a native user of the Cyrillic script - although I read it), if the Bulgarian version wasn't labelled as such, I would not even notice the difference. Yes, some letters - mainly minuscule - have some specific features, but most of the time they closely resemble the hand-writing script I had learned on my Russian classes decades ago.
This resembles me an effort to create a native Polish script by a graphic designer a decade or so ago. He shaped the letters - and their "hints" in the font files - so that they look nicely in combinations in which they are often used in the Polish language, like "rz", "sz", "cz", "ło", etc, which are rarely or never used in English, and hence they are unoptimised for this usage in commercially available font sets. A whole lot of the hard work, but the final effect is barely noticeable for the persons without education in graphic or design - and as far as I am aware, the number of users is rather limited, since most of the time default Windows fonts are used anyway.