Where bye bye come from?

Answer 1

It is a very informal form of good-bye/goodbye, but is only used between people who are familiar with each other.

'Bye bye' is sometimes described as the baby-talk reduplication of 'bye'. ('Bye' is an informal way of saying 'Good-bye.')

Good-bye is said to be an abbreviation of God be with you, although it could just mean 'Good travel', from good + by, as in "Long labors both by sea and land he bore." (--Dryden) Here 'by' means 'in traversing'. i.e. "Long labors in traversing sea and land he bore." So 'good by' could mean 'I hope all your traversing is good.'

Either way, the expression was used as an invocation of holy protection for a journey or time apart.

In 1573, goodbye was written as godbwye, changing to goodbye in 1591.

Example of bye-bye: Woman speaking to her grandchildren:- Bye bye, my darlings! Come again soon!