Perhaps from ba'ah (in the sense of asking); properly, a request; used only adverbially (always with "my Lord"); Oh that!; with leave, or if it please -- alas, O, oh.
see HEBREW ba'ah
בִּי particle of entreaty, craving permission to address a superior, always followed by אֲדֹנִי (or אֲדֹנָי), and always (except Joshua 7:8) at the beginning of a speech, I pray, excuse me — (not improbable from √ ביי; so that אֲדֹנִי בִּי will be literally a supplication of (i.e. to my lord! compare Wetzst l.c., who compares the Arabic literally a prayer to my lord! a standing formula = Pray, excuse me, used exactly as אֲדֹנִי בֹּי. According to other contracted from בְּעִי, from בָּעָה to ask, and so literally a petition! compare Aramaic בְּבָעוּ, (e.g. Genesis 19:18 ᵑ7, Numbers 12:13 ᵑ6); but ע is not often elided in Hebrew) — Genesis 44:18 יְדַבֶּרנָֿא אֲדֹנִי בִּי I pray, my lord, let thy servant speak, etc.; so Numbers 12:11; Judges 6:13; 1 Samuel 1:26; 1 Kings 3:17, 26, and following by a plural subject Genesis 43:20 א ׳בִּי יָרַדְנוּ יָרֹד Oh, my lord, we came down, etc.; אֲדֹנָי בִּי (to God) Exodus 4:10, 13; Joshua 7:8; Judges 6:15; 13:8 (ᵐ5 in Pentateuch and Joshua δέομαι, δεόμεθα: in other books absurdly ἐν ἐμοί).