Bye-bying is a colloquial term that refers to the act of saying goodbye, leaving or departing from a certain place or situation. It is important to have a diverse vocabulary to avoid repetitive language and help convey precise meanings. Some synonyms for bye-bying include bidding adieu, saying farewell, taking leave, parting ways, or simply goodbye. Other alternatives can be saying cheers, see you later, catch you on the flip side, until next time, or peace out. It is always important to be polite and considerate when leaving and choosing the appropriate term to use when saying goodbye.