I see a chicken and egg situation between Frederick & Anne. They are both keeping their distance from each other BECAUSE that's the behaviour they see from the other person.

All we know of their first meeting is "Her eye half met Captain Wentworth's, a bow, a curtsey passed; she heard his voice; he talked to Mary, said all that was right; said something to the Miss Musgroves, enough to mark an easy footing; the room seemed full, full of persons and voices, but a few minutes ended it. Charles shewed himself at the window, all was ready, their visitor had bowed and was gone, ..."

Since she already knows Frederick, it's certainly within the bounds of propriety to initiate a conversation. "Do you find the neighborhood much changed since you were last here?"

Elizabeth Bennet or Emma would have found a way to open the conversation.