Actually IS also the Japanese for "bye-bye". As anyone who speaks any language on Earth knows, there are a number of ways to say "goodbye" in every language -- and "sayonara" is but one in Japanese (and a pretty stuffy one, at that).
See ja.wikipedia.org/wiki/バイバイ for concrete evidence.
Hey everybody, let's not talk about things we don't understand!!
Just correcting the other definition for this phrase, "bai bai" is NOT Japanese for "bye bye". If you have to put it as an Asian language, it's Chinese for "bye bye". When you say "bye bye", in Chinese it sounds like words that have Chinese pinyin (the system that helps you to read Chinese words) for "bai bai".