"dust-sweeper, a brush for sweeping," late 14c., also, c.1400, "brushwood, brushes;" from Old French broisse (Modern French brosse) "a brush" (13c.), perhaps from Vulgar Latin *bruscia "a bunch of new shoots" (used to sweep away dust), perhaps from Proto-Germanic *bruskaz "underbrush."
"shrubbery," early 14c., from Anglo-French bruce "brushwood," Old North French broche, Old French broce "bush, thicket, undergrowth" (12c., Modern French brosse), from Gallo-Romance *brocia, perhaps from *brucus "heather," or possibly from the same source as brush (n.1).
late 15c., "to clean or rub (clothing) with a brush," also (mid-15c.) "to beat with a brush," from brush (n.1). Related: Brushed; brushing. To brush off someone or something, "rebuff, dismiss," is from 1941.
"move briskly" especially past or against something or someone, 1670s, from earlier sense (c.1400) "to hasten, rush," probably from brush (n.2), on the notion of a horse, etc., passing through dense undergrowth (cf. Old French brosser "travel (through woods)," and Middle English noun brush "charge, onslaught, encounter," mid-14c.), but brush (n.1) probably has contributed something to it as well. Related: Brushed; brushing.