Etymology

According to Abraham ibn Ezra (in his short commentary to Genesis 43:20 ), the particle comes from the preposition, and is short for something like "the sin is mine", meaning "I sin in speaking, so do to me what you will, but hear me out". According to Nachmanides (in his commentary ad loc.), the particle does not exist as a separate sense; rather, all instances of בִּי אֲדֹנִי ‎(bí adoní) are to be translated "master over me", and similarly wherever else בִּי appears, which is thus just the preposition form.