Good-bye to All That author's initials (2-2)
I believe the answer is:
ta-ta
'good-bye' is the definition.
'to all that author's initials' is the wordplay.
'initials' suggests taking the first letters.
The initial letters of 'to all that authors' is 'TA-TA'.
(Other definitions for ta-ta that I've seen before include "Cheerio" , "A Farewell" , "Bye-bye" , "Bye!" , "Adieu" .)