Also by-by(e, bye bye, 8 buy buy and simply by. A colloquial and nursery variant of GOOD-BYE.
1709. Tatler, No. 2. For Hat and Sword Hed call, Then, after a faint Kiss,cry, By, Dear Moll: Supper and Friends expect me.
1736. Bailey, By by, usd familiarly, and chiefly to Children, instead of Good by or God be with you.
a. 1745. Swift, Wks. (1768), VI. 320. Buy, Buy, Nic, not one poor smile at parting.
1777. Sheridan, Sch. Scand., III. i. I shall interrupt youso bye! bye!
1872. Lever, Ld. Kilgobbin, xiv. (1875), 95. By-by! said Atlee, carelessly, and he strolled away.