I agree that initially I thought it odd that for all Emma's new good intentions she did not say "I'm sorry". But I kept thinking about how she would go about it. To apologise directly would be awkward in her admission of wrong in her action but more for Miss Bates in Emma's reminding her that she was considered tedious & ridiculous. The tacit apology of her early visit I think was understood by both.

In addition, more important than apology to contrition is repentance which is not exactly the same thing. Contrition is being sorry about the action. Repentance is a resolve to change one's behavior in future. I think JA indicated that Emma fully planned to avoid both ungenerous actions and ungenerous thoughts about Miss Bates in future, & recognized her own inferiority to Miss Bates in the area of good will, and allowed Miss Bates the position of forgiveness & "heaping live coals on her head" in her persistent praise & gratitude.