Usage of "bye bye"
Hello.
I was watching an episode of "The Venture Brothers" and there was a character who ended a telephone conversation with "bye bye" and another character looked at him as if he were saying some childish thing to which the former replied, "he said it first".
I was taught in elementary school that the thing to say when you end a conversation is "bye bye".
¿Was this wrong, or has it changed?
9 Answers
Most adults would say "good bye" or just "bye" or even "bye for now" where as children often say "bye bye" and occasionally an adult might say "bye bye" to a child or a close friend.
The term "bye bye" has come to be used in situations where the speaker wants to imply extreme friendliness even when talking to strangers. One of the big useages is when flight crews bid their passengers good - bye. Otherwise, it is used when dealing with children.
Saying "bye bye" is usually used with children or like Rich said, with a close friend. A common variant is "buh-bye", which can be used with anyone. It isn't formal, though. Another common phrase is "bye bye now", which I would say isn't childish sounding, it's just a phrase you'd reserve for usage on the phone with friends.
I can't add much to the very good answers already offered, but will comment that it was no doubt just the right thing to teach to an elementary school student, as they tend to be children -- except for the truly unsuccessful ones 
I will add that you'll hear women use it a bit more than men, which I'm sure is a standard males-not-wanting-to-sound-weak/childish cultural thing. When used by/among adults, it connotes a feeling of intimacy.
I've learned something new. Thanks comunacho for asking :D
ha, thanks for that question, now I've learned something,too and will never say "bye bye" again
Bienvenidos a Inglaterra;
Decimos 'bye bye' todo el tiempo.
In England, you hear it all the time: Bye bye, see you next week, bye then, bye, goodbye, bye, take care, bye, chao..
It's maybe slightly out of fashion but I don't think anybody will notice if you keep using it. If in doubt say çao'.
End all texts with x or xx ( obviously two kisses are more friendly than one).
Bye is hardly ever used in texting. Nor in e-mails or business letters, obviously. But in the street, it's still very normal.
Bye for now.
What every one else has said is true. Also, I think it depends on the intonation.
If I were to say: BYE-bye, with just a little more emphasis on the first "bye", it sounds more childish. But more similarly to what elektrisk564 mentioned - "bye bye now", where the emphasis is like so: bye-BYE-now, it doesn't sound so childish anymore (perhaps as much to do with the addition of "now" as with the emphasis falling on the second "bye".) If you say "bye bye" in the same way you'd say "ta-ta" ("bye-BYE" and "tah-TAH") it doesn't sound childish
I have learned something new today, I say bye, bye in English and I say chao, chao in Spanish.
