Where does “bile” come from?

bile (Middle English) comes from Old English bȳl, from Proto-Germanic būlō, from Proto-Indo-European bʰel-, from Proto-Indo-European bʰōl-.

Ancestry of “bile”, step by step

Step	Language	Word	Meaning
1	Old English	bȳl	—
2	Proto-Germanic	būlō	boil; sore
3	Proto-Indo-European	bʰel-	to sound; to speak, roar, bark; shiny, white; to...
4	Proto-Indo-European	bʰōl-	—

bile — Etymology, Origin & Word History | Etymology Explorer