What's the "een" in Halloween?
probably a merger of two old words: The sense in bid farewell is from Old English biddan "to ask, entreat, pray, beseech; order; beg" (class V strong verb, past tense bæd, past participle beden), from Proto-Germanic *bidjan "to pray, entreat" (cf. German bitten "to ask," attested from 8c.), which, according to Kluge and Watkins is from a PIE root *gwhedh- "to ask, pray" (see bead (n.)).
To bid at an auction, meanwhile, is from Old English beodan "offer, proclaim" (class II strong verb; past tense bead, p.p. boden), from Proto-Germanic *biudanan "to stretch out, reach out, offer, present," (cf. German bieten "to offer"), from PIE root *bh(e)udh- "to be aware, make aware" (cf. Sanskrit bodhati "is awake, is watchful, observes," buddhah "awakened, enlightened;" Old Church Slavonic bljudo "to observe;" Lithuanian budeti "to be awake;" Old Irish buide "contentment, thanks"). As a noun, 1788, from the verb.
Old English bidan "to stay, continue, live, remain," also "to trust, rely" (cognate with Old Norse biða, Old Saxon bidan, Old Frisian bidia, Middle Dutch biden, Old High German bitan, Gothic beidan "to wait"), apparently from PIE *bheidh-, an extended stem of one root of Old English biddan (see bid (v.)), the original sense of which was "to command," and "to trust" (cf. Greek peithein "to persuade," pistis "faith;" Latin fidere "to trust," foedus "compact, treaty," Old Church Slavonic beda "need"). Perhaps the sense evolved in prehistoric times through "endure," and "endure a wait," to "to wait." Preserved in Scotland and northern England, replaced elsewhere by abide in all senses except to bide one's time. Related: Bided; biding.
Latin bis in die (twice a day)