i Register
In some senses, bye-bye is marked as informal, colloquial. Watch for register when choosing this word.
intj
Goodbye.
Bye bye! Let's play again some time!
noun
A goodbye.
Bedtime for a toddler, going to sleep, going to bed.
Brush your teeth, it's time to go bye-bye.
"[H]e came to the gate of the city; and finding it shut lay him down and went to by-by!"