Standard goodbyes
3 再见 goodbye (standard) (literally "see again")
拜拜 bye-bye (borrowed from English, very common)
拜 bye (short form, among friends)
Depending on when you'll meet again
5 回头见 see you later (when you'll see them later today)
一会儿见 see you in a moment (in a few minutes)
明天见 see you tomorrow (meeting tomorrow)
下次见 see you next time (no specific date)
后会有期 we'll meet again someday (more literary, for a long separation)
Formal or leaving formulas
4 我先走了 I'm heading off first (when leaving a meeting before others)
我先告辞了 I take my leave (formal, professional)
失陪了 excuse me for leaving (very polite, formal)
保重 take care (warm, for a long separation)