The word "bye-bye" is a duplication of "bye" and both are more likely to be used between people who are very close-say members of a family-than between more formally related people.

“ bye - bye ”这个词和它的简洁版“ bye ”一样，更多地在彼此十分亲密的人之间使用，比如亲戚，而对关系正式的对象就很少用了。

youdao

I will. Bye-bye! Bye!

我会的。再见。再见！

youdao

Take care, sonny! I will. Bye-bye! Bye!

孩子，当心！我会的。再见。再见！

youdao

I said good-bye and left. "The man who almost had an accident was one of my servants.

VOA: special.2009.12.26

We'll say good-bye to him here in our course.

本课程中,我们要跟他再见了

耶鲁公开课 - 聆听音乐课程节选

Bye-bye now.

拜拜了。

哈佛公开课 - 计算机科学课程节选

Which is why you might say that it's either bye-bye eurozone, because the costs for borrowing of an unreformed eurozone remain prohibitively high, or it's bye-bye eurozone, because it turns into something that looks more like a giant single country.

BBC: The eurozone's borrowing costs may stay lethally high

So wave bye-bye to everything you knew and set out as you would for a good holiday.

BBC: NEWS | UK | Magazine | Advice for dads? Work it out yourself

Mr. JARRETT: I haven't been in the studio for probably since Bye-Bye BlackBird.

NPR: Keith Jarrett's Audience Connection