I agree with Odeda that Bat-Zion is part of her given name (or perhaps her "maiden name").  One should note that the name Batya, would have been pronounced by Ashkenazim as Basya, from which Bessie is an obvious Anglicization.  Bat-Zion would have been pronounced by Ashkenazim as Bas-Zion, which shares some of that same sound play.

Tangentially, another recent headstone query featured the Hebrew name Pesha and English Bessie, which is a similar Anglicization.  Pesha is a Yiddish form of Batya, often informalized to Pessie, which then easily turns into Anglicized Bessie.  P/B swaps are a known linguistic phenomenon.

-Ittai Hershman
 New York City