Answer by Professional Japanese Teacher
Excuse me for leaving first.
Sayoonara is the direct equivalent for “good bye” but this is not commonly said by the Japanese. It has the implied meaning that you are not going to see the other person for a long time, so that is probably why your Japanese supervisor was surprised to hear it.
For workplaces, it is better to use the more formal phrase above. Your supervisor was being friendly in saying “じゃ、またあしたね Ja mata ashita ne (see you tomorrow)” but you should not use the same phrase for her as you are in a formal workplace.
For more essential greetings in Japanese in Japanese, check out our following article.
8 Essential Japanese Greetings for Japanese beginners