"outward bound," 1590s, from out- + bound (adj.2).
Entries linking to outbound
out-
in Old English a common prefix with nouns, adjectives, adverbs, and verbs, "out, outward, outer; forth, away," from out (adv.). The use was even more common in Middle English, and also with the senses "outer, outside, on the outside, from without, external, externally; apart; greatly, extremely; completely, thoroughly, to completion." Other senses of out that extended into the use as a prefix include "beyond the surface or limits; to the utmost degree; to an explicit resolution."
In composition out has either its ordinary adverbial sense, as in outcast, outcome, outlook, etc., or a prepositional force, as in outdoors, or forms transitive verbs denoting a going beyond or surpassing of the object of the verb, in doing the act expressed by the word to which it is prefixed, as in outrun, outshine, outvenom, etc. In the last use especially out may be used with almost any noun or verb. [Century Dictionary]
bound adj.2
c. 1200, boun, "ready to go;" hence "going or intending to go" (c. 1400), from Old Norse buinn past participle of bua "to prepare," also "to dwell, to live," from Proto-Germanic *bowan (source also of Old High German buan "to dwell," Old Danish both "dwelling, stall"), from PIE root *bheue- "to be, exist, grow." The final -d is presumably through association with bound (adj.1).