Think of buxsome as bow-some (willing to bow to). Like all of the best words, it's from old english.

Nice has obscure origins, probably in old French. It also means extravagent, lecherous, or foolish. But as usually glossed in the English Renaissance, it's "being overly attentive to detail." I don't know if anyone knows a clear origin for the word. At least my OED doesn't.