There are several synonyms for the word "byebying" such as "farewelling," "parting," "adieu-ing," "bidding adieu," "saying goodbye," and "taking leave." All these words signify the act of parting ways or saying goodbye to someone or something. Although they all convey the same meaning, each word has a different tone and level of formality. "Farewelling" and "adieu-ing" are more formal than "saying goodbye," which is commonly used in everyday speech. On the other hand, "taking leave" is more practical and straightforward, while "parting" is more poetic. All in all, these synonyms can help in expressing one's farewell message effectively in different contexts.