"stiff, coarse hair of certain animals," especially those set along the backs of hogs, Old English byrst "bristle," with metathesis of -r-, from Proto-Germanic *bursti- (source also of Middle Dutch borstel, German borste, Danish börste), from PIE *bhrsti- from root *bhars- "point, bristle" (source also of Sanskrit bhrstih "point, spike"). With -el, diminutive suffix. Extended to similar appendages on some plants and insects.

"rough sound of the letter -r-" (especially that common in Northumberland), 1760, later extended to "northern accented speech" in general. Possibly the sound of the word is imitative of the speech peculiarity itself, or it was adapted from one of the senses of bur (q.v.), perhaps from the phrase to have a bur in (one's) throat (late 14c.), which was a figure of speech for "feel a choking sensation, huskiness." OED says the Scottish -r- is a lingual trill, not a true burr.

common name of a kind of coarse, weedy plant, 1590s, from bur + dock (n.3).

mid-15c., "small knot in cloth or thread," from Old French bourle "tuft of wool," which perhaps is related to the root of bur, or from Vulgar Latin *burrula "small flock of wool," from Late Latin burra "wool," a word of unknown origin. In American English also "a knot or excrescence on a walnut or other tree" (1868).

mid-15c., "full of burs;" see bur + -y (2).