In the context of the story, Wyatt Earp and his brothers (dead and injured) are having to leave town. The Cowboys gang leader (E. Powers Boothe played), is the height of disdain and dismissal of their enemies... and says... “Well, Bye”
He could literally not care less— they are defeated.
Very well done.
Except they aren’t defeated. It’s a ruse by Wyatt, knowing the cowboys will come after them, to get his brother out of town and to show his new US Marshal’s badge (”You tell ‘em I’m comin,’ AND HELL’S COMIN’ WITH ME.”)