Ta ta for now is English See you later dude is American

I don't know if it's so much 'formal' as it might just be 'posh'. It always reminds me of Tigger on "Winnie the Poo". Gives "ta-ta" a goofy feeling.

Ta ta for now is British English, yes. :) However, I'd say it's only usually used amongst the 40+ age group/richer people in society. It's very, very formal.