Judging by the native transcription and the sound of the name, it is clearly not a Hebrew diminutive, but a Yiddish one. [noted -ed] The Hebrew should be בשה/באשה and not באשע, as ע is typically used in Yiddish for names ending in e. (I am a native Hebrew speaker who's studying Yiddish)Take Basha for example which is a variant of this name but is listed as Yiddish according to this site.https://www.behindthename.com/name/basha/submitted
From what I have found, Bashe can also be spelled Basha or Basia. Each are Polish and Slavic variations of Barbara.
― Anonymous User 6/7/2020
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The origin of the word BASHE is discussed among the Jewish scholars. They are of the opinion that it does not originate from the name BATYA, but that people who were named BATSHEVA were referred to as BASHE.
Take Basha for example which is a variant of this name but is listed as Yiddish according to this site.
https://www.behindthename.com/name/basha/submitted