==I don't think Bat Shem Tov is in the running.
1. The patach vowel of Bat would generally not be part of the abbreviation
2. Women weren't generally accorded surnames based on a father's name,
though their personal names could be converted into family names.
Michael Bernet, New York
As you have discounted Bat Shem Tov for the probable origin of BAST, could
it be possible (likely) that this was another form of contraction of BAal
My family are, AFAIK, all Dutch and Sephardic (>from the habit of naming
after living grandparents) and have no known Hasidic or German connections.
Would the name (epithet) Ba'al Shem Tov have been used by them?
Henry Best [London]