'Ta-ta' is a light, cheerful way of saying goodbye. It is British, and it has a particular flavour: slightly old-fashioned, slightly childish, and very warm. Grandmothers say it, people say it to small children while waving, and friends say it to each other half-jokingly, the way you might sing out a goodbye rather than just state one. It suits short, easy partings — leaving a shop, hanging up the phone, stepping off a bus. It does not suit serious ones; nobody says 'ta-ta' at an airport when someone is leaving for two years. Because of that playful edge, using it with a boss or a stranger in a formal setting would sound odd, as if you were being deliberately silly. In the north of England it is especially common, and there is a related phrase 'ta-ta for now' (sometimes shortened to TTFN), which means 'bye for a while, see you soon'. Spelling: two syllables joined by a hyphen, and both are said with the same light bounce. Note that although it looks like the 'ta' that means thanks, in this word it has nothing to do with thanking — a coincidence of sound, not a shared meaning.