Old English bosm "breast; womb; surface; ship's hold," from West Germanic *bōsmaz (source also of Old Frisian bosm, Old Saxon bosom, Middle Dutch boesem, Dutch boezem, Old High German buosam, German Busen "bosom, breast"), perhaps from PIE root *bhou- "to grow, swell," or *bhaghus "arm" (in which case the primary notion would be "enclosure formed by the breast and the arms"), or possibly a word from a substrate language.
Bosoms in the narrowed or euphemistic meaning "a woman's breasts" is from 1959; bosomy "big-breasted" is from 1928 (earlier of rolling hills, etc.). Bosom-friend is attested 1580s; bosom buddy from 1924. Abraham's bosom "the abode of the blessed" is from Luke xvi.19-31.