The phrase 'Ta-ta for now' is not generally used in English language anymore, at least not by the majority of people. It is seen as a posh phrase, mainly used by upper class women.
I personally say, 'See you later' or simply, 'Bye'. A lot depends on your age range, social status and the relationship you have with your friend. A young person might say 'Laters', or 'In a bit', where as older people tend to be more formal, saying, 'Good bye' or, 'See you soon'.
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