mid-13c., from Anglo-French buquet "bucket, pail," from Old French buquet "bucket," which is from a Germanic source, or a diminutive of cognate Old English buc "pitcher, bulging vessel," originally "belly" (buckets were formerly of leather as well as wood), both from West Germanic *buh- (cf. Dutch buik, Old High German buh, German Bauch "belly"), from PIE *bhou-, variant of root *bheu- "to grow, swell" (see be).
Kick the bucket "to die" (1785) perhaps is from unrelated Old French buquet "balance," a beam from which slaughtered animals were hung; perhaps reinforced by the notion of suicide by hanging after standing on an upturned bucket (but Farmer calls attention to bucket "a Norfolk term for a pulley").
To speed; barrel: The kids were bucketing along (1860s+)
brain bucket, someone can't carry a tune in a bucket, drop one's buckets, for crying out loud, go to hell in a handbasket, gutbucket, kick the bucket, lard-bucket, rust bucket, sleaze-bucket, slimebag
a vessel to draw water with (Isa. 40:15); used figuratively, probably, of a numerous issue (Num. 24:7).