First: language question: Did goodbye come from God Bye? And what does bye mean? Or Did it mean.
Now it’s clear that bye is just a leave taking. I wonder if it once meant something else.
Second: This line makes me think of how impossibly awkward it can be to part company with someone, how hard it is to say, “Leave me alone” how hard is it to say, “This conversation needs to be over now.” There are times when it must be nice to be a king – to say simply, “You’re dismissed.” And you are free. I’m not sure how gracefully Hamlet’s managing it here.