Green’s Dictionary of Slang

to say goodbye, to leave.

1904		Sun. Times (Perth) 11 Dec. 1/1: She ostentatiously sees he doesn't meet with mishaps by affectionately ta-ta-ing him at the train.
1932		(con. 1910s) J.T. Farrell Young Lonigan in Studs Lonigan (1936) 100: Then Leon ta-taed along, pausing to ask Studs about taking music lessons.