"Thank you, bye-bye" can be said in Engpsh as "Thank you, bye".
The origins of "bye" as a casual farewell is bepeved to have originated in the 1650s as a shortened form of "God be with ye".
Example sentences in Engpsh with Chinese translations:
"Thank you for coming, bye!" -- 谢谢你来，再见！
"It was great talking to you, bye." -- 和你聊得很好，再见。
"Have a great day, bye." -- 祝你有美好的一天，再见。