Douglas Harper's Etymology Dictionary
also tata, "good-bye," familiar salutation in parting, 1823, a word first recorded as infant's speech. Abbreviation T.T.F.N., "ta-ta for now," popularized 1941 by BBC radio program "ITMA," where it was the characteristic parting of the cockney cleaning woman character Mrs. Mopp, voiced by Dorothy Summers.
Wiktionary
interj. (alternative form of ta ta English)
Usage examples of "ta-ta".
Continuing to ignore Peter, Ta-Ta pulled the skirt of her Mother Hubbard around her legs and sank to the step that Peter had vacated, as if he had done it for her.
And if you take, Ta-Ta, if in nine months' time you give me a nice little nigger baby, that necklace you have around your throat right now is yours to keep for ever and ever.
As Selby bumped along in the wagon now, he scratched nervously at his red Vandyke beard and realized that he had not heard as much as a word from Ta-Ta.