From Middle English boote, bote, from Old French bote ("a high, thick shoe"). Of obscure origin, but probably related to Old French bot ("club-foot"), bot, from Old Frankish *butt, from Proto-Germanic *buttaz, *butaz, from Proto-Indo-European *bʰewt-, *bʰewd-. Compare Old Norse butt ("stump"), Low German butt ("blunt, plump"), Old English bytt ("small piece of land"), buttuc. More at buttock.
From Middle English boote, bote, bot, from Old English bōt ("help, relief, advantage, remedy; compensation for an injury or wrong; (peace) offering, recompense, amends, atonement, reformation, penance, repentance"), from Proto-Germanic *bōtō ("atonement, improvement"), from Proto-Indo-European *bʰed- ("good"). Akin to Old Norse bót ("bettering, remedy") (Danish bod), Gothic 𐌱𐍉𐍄𐌰, German Buße. bote (a borrowing from Middle English).