This sense of bucket probably comes from the Old French buquet, meaning a trébuchet or balance. The more familiar sense of pail is likely from the Old French buket, meaning a tub or pail.
Puts me in mind of dear Hyacinth.
Whenever a Big List entry is revised I discover that it’s full of fascinating info that is new to me. I really must browse the List more, it’s an etymological treasure-chest right under my nose and because of that I sometimes forget it.