According to A Dictionary of Surnames by Patrick Hanks and Flavia Hodges, the Jewish (Ashkenazic) origins of the name are obscure. They do say when the name appears it is found in areas where English influence is highly unlikely, so it could not be thought of as an Anglicization of a Jewish surname. Their best guess seems to be that it's a combination of naming elements using a male name beginning with "B" and a part of a Hebrew surname "bar-" (meaning 'son of ..."). They don't mention nationality, but my understanding of the meaning of Ashkenazic is that they come from some part of Germany. I could be wrong.