Meaning of BaSaki(バ先)
BaSaki(バ先) is an abstraction for “Baito Saki(バイト先)” which means workplace (Place of one’s part-time job).
“Baito(バイト)” means part-time job and “Saki(先)” means place in this case.
This is a slang among young people.
Example Conversation
A: Are you dating anyone?
B: Yeah, I’m dating with a part-time coworker.
A: Sounds nice, maybe I should find part-time job…
A: そういえば今誰かと付き合ってるの?
B: バ先の人と付き合ってるよ
A: いいなぁ、私もバイトしようかなぁ