Hi Miles,
Bavaria Beer we drink. No I do not believe the B for the city of Batavia.
Batavia Dutch East Indies; from 1619 to 1949 under the name of the current Indonesian capital Jakarta was the seat of Authority in the Dutch East Indies. Two years after the founding of Batavia an European silversmith worked in Batavia. In Batavia, European silversmiths were subject to an ordinance on the gold and silverwork, although the native masters were exempt. There was no Batavia silversmith guild as such, but the gold and silver have been tested and punched with a city mark; an upright sword in a laurel wreath.

In 1634 the Assay Office has been assigned to a goldsmith who also acted Assay Master. The first comprehensive instruction dates from 1667. Initially a date letter has been used, but the date leter disappeared around 1730. The assaying of gold and silver stopped around 1800.
Gratitude free tranlated into English out of the book ; Het Zilver lexicon by Janjaap Luijt
Regards,
Oel