"fastened," mid-14c. in figurative sense of "compelled," earlier in fuller form bounden (c. 1300), past-participle adjective from bind (v.). Meaning "under obligation" is from late 15c.; the literal sense "made fast by tying (with fetters, chains, etc.)" is by 1550s. In philology, designating a grammatical element which occurs only in combination with others (opposed to free), from 1926. Smyth has man-bound (1867), of a ship, "detained in port for want of a proper complement of men."
From mid-14c. as "an external limit, that which limits or circumscribes;" figuratively, of feelings, etc., from late 14c. From late 14c. as "limits of an estate or territory." Now chiefly in out of bounds, which originally referred to limits imposed on students at schools; the other senses generally have gone with boundary.
"to leap, spring upward, jump," 1590s, from French bondir "to rebound, resound, echo," from Old French bondir "to leap, jump, rebound;" originally "make a noise, sound (a horn), beat (a drum)," 13c., ultimately "to echo back," from Vulgar Latin *bombitire "to buzz, hum" (see bomb (n.)), perhaps on model of Old French tentir, from Vulgar Latin *tinnitire.
c. 1300, from the noun, replacing Old English sniwan, which would have yielded modern snew (which existed as a parallel form until 17c. and, in Yorkshire, even later), from the root of snow (n.). The Old English verb is cognate with Middle Dutch sneuuwen, Dutch sneeuwen, Old Norse snjova, Swedish snöga.
Also þikke as snow þat snew,
Or al so hail þat stormes blew.
[Robert Mannyng of Brunne, transl. Wace's "Chronicle," c. 1330]
The figurative sense of "overwhelm; surround, cover, and imprison" (as deep snows can do to livestock) is 1880, American English, in phrase to snow (someone) under. Snow job "strong, persistent persuasion in a dubious cause" is World War II armed forces slang, probably from the same metaphoric image.