"Ta-ta" (short "A" on first "ta", long on second) is the correct form (hyphen optional). It's supposedly derived from a nursery form of valediction. "TTFN" goes back to a popular wartime radio show, ITMA [It's That Man Again], with comedian Tommy Handley, and reflects the BBC's obsession with initials. "Ta-ta" goes back a much longer way, and there was a music hall song, Put on your ta-ta, little girlie [... and come for a ta-ta with me]; here the meaning has been extended to include "hat" and "walk". The second "T" is elided in some areas to give "Tarra", or even "Traa".

You came to the right place, Snuffy!

Steve