-there are two interpretations available in academic resources:

First one is that the surname is derived from the name of the ancient tribe from the Bessarabia region in Moldova.

http://en.wikipedia.org/wiki/Bessarabia

Second onomastic interpretation is tied to the localized branch of surname in former Yugoslavia among ethnic Serbs - it stems from the word "basara" denoting a traditional household object in which the milk product called "basa" was made.





Serbian Genealogy Society SGS "Rodoslovlje"
http://www.rodoslovlje.com/en