Kalojan,
Sure, this is not a bow type used in Balkans at the time you mentioned. Composite bows in Balkan peninsula had more turkic/Kipchac characteristics/influences. Ears are of smaller dimension judging by painted records, no knees, reflex at the grip goes between 160 and 150 degrees, in some cases less, ears and grip are often strenghten by bone plates (i am talking about most Serbian bows, Bulgarian ones do not have bone stiffeners).
Most of depicted bows seem to be covered by birch bark lacquered in white on the belly side (olifa) and also leather covered back painted in different colors. Olifa is lacquer mentioned in several Serbian medieval manuals such as Erminia by greek zograph Dionisius of Furna, Serbian Erminia and Tipicon of Nectarius.There's also manuals for making colors (not for painting the bows but it can explain how colors for (even) bows decorations were prepared).
Interesting that Serbs, Greeks and Bulgarians used lead for making white color (same as Tan T'an Chiung reports about bowmaking in Chengtu).
I believe that this bow came to museum from some other collection as it is case of some artefacts in Serbian museums ( i had a chance to see two unexposed Chinese bow in the museum's store.
There's no so much representation of Bulgarian bows in mural painting as it is in Serbian or Greek mural painting but you should start with mural painting. Check this topic i started long time ago. You can notice something like a birch bark cover over the back of the bow(s)
http://atarn.net/phpBB2/viewtopic.php?t ... rbian+bows
Cheers!