Genetics and physical anthropology of Bulgarians have no link to Central Asian Turkics whatsoever.
Most are Pontid, meaning that they are similar to many Romanians, Southern Ukrainians/Russians, some Greeks and some Georgians. Genetically, they do not differ from neighbouring states (ironically enough, they cluster far only from neighbouring Turkey).
I would even suggest that ancient Bulgars were not Turkic either, but some ancient Iranian horde, like Scythians or Sarmatians.
Nowadays one sees Bulgarians using ancient Bulgar names like Asparuh, Krum, Kubrat and Tervel (much like Hungarians use ancient names of their Hunnish ancestors – who I also don't believe to be Mongol, as some claim, rather Iranic – like Réka and Atilla), which could very well be similar to names our ancient Scythians and Sarmatians used, except Bulgarians have resurrected them and use them alongside Slavic names like Vladimir, Svetoslav and Velislava and Christian names like Lazar, Ivan, Anna, Maria and Ekaterina.
Otherwise, Sokil summed it up as he usually does: short, brash, effective and painfully true.