Emma's showing up at Miss Bates' is a show of remorse in itself. She has no reason for coming except to show that remorse. When she's been at Miss Bates' house before, it was always in someone else's company (and with some ulterior motive--although Miss Bates probably didn't know that).

What she might have said if the conversation had not turned to Miss Fairfax will always be unknown, but I don't think she would have said, "I apologise for what I said yesterday. It was wrong and I can only beg that you forgive me."

It just doesn't feel like something Emma could say to Miss Bates without making Miss Bates feel extremely uncomfortable. To bring the statement up again would only cause further embarrassment, and a genuine change in how Emma treats Miss Bates is the kindest thing Emma can do to show her remorse. When Emma thinks, "In the warmth of true contrition, she would call upon her the very next morning, and it should be the beginning, on her side, of a regular, equal, kindly intercourse." She is making up her mind to an unspoken apology that is quite real and just as understandable as any.

At least that's the way I see it.