The best explanation for the origins of the Coventry Carol can be found Here.

As for the last verse, if it is "dialogue" from a play as described in the link, it seems like Mary is saying, "oh, woe is me, poor child! And I'll keep mourning and saying 'woe is me'until your departure, but I won't sing, 'Bye bye.... Etc."
Of course, trying to parse it with that much detail takes all the poetry and beauty out of it.