bye-bye(n = noun.communication) adieu, adios, arrivederci, au revoir, auf wiedersehen, bye, cheerio, good day, good-by, good-bye, goodby, goodbye, sayonara, so long - a farewell remark; "they said their good-byes"
is a kind of farewell, word of farewell

bye-bye, int. colloq. = GOODBYE.

bye-bye, n. (also bye-byes) (a child's word for) sleep.

Etymology:
ME, f. the sound used in lullabies