Ah, feuds. Sometimes they do start up from more than just petty irritations and grievances. I wouldn't trust an apology from Augustus to mean anything unless it came with penalties, obligations he can't just squirm out of, or restitution anyway; he's shown himself to be very free with saying whatever he likes to get people to do what he wants.
Yeah, I would agree that Bettina would be fully justified in never, ever trusting him or working with him again. Which may have been his intention after all. Three dimensional chess, man.
But at the end of the day Augustus is secondary to where this scene goes.
but
It is a good starting point.