"bye now" is a correct and usable phrase in written English.
You can use it when saying goodbye, such as in the sentence: "It was great to talk with you! Bye now!".
Bye bye, now," read an especially pithy one.
At present, my dear, I must bid you good bye; Now, do as you're bid; and, remember, don't cry.
"Bye, bye now," Dr. Tassone called out in reply to a goodbye uttered by someone in Mr. Costigan's group.
But if she's getting a bye now, she will not from the Republican standard-bearer, whoever he may be.
Opening a conversation with: "What's your most favourite yummy yum snack?" and ending it with "I've got to go bye-bye now" was not always a success with the grown-ups.
Among them are mandatory physical attendance at all board meetings ("Two missed meetings and you're out"); thorough preparation ("Do not think you can learn about the issues by listening to the management presentations; we don't do them"); development of company and industry knowledge; and time commitment ("If you can't spend 15 working days a year for this board, let's say good-bye now").
The Zeitgeist has spoken: "Buh-bye now".
Time for beddy-bye now, big boy, and someday, if you're very, very good, Santa Clause just might bring you a brain for Christmas.
"How do you like your blue-eyed boy, Mr. Death?" Good-bye for now, old friend.
