Up to that point, Catherine's behaviour as seen by Henry has been flip-flopping. It's timely that he should do some prodding.

Chapter 3. She visibly enjoys his conversation. Encouraging. She's discerning enough to do 'that shake of the head'. Encouraging -- and he can probably guess what it was about. She's only been in Bath about a week, so is likely still to be there when he returns.

Chapter 8. She's slow getting back to her party after the first pair of dances. Discouraging -- and consistent with deliberately avoiding him, even though he behaved himself and didn't noodle around with Mrs Allen's foibles this time.

Chapter 10/Wednesday. She gives Eleanor 'some knowledge of her new acquaintance’s feelings'. Encouraging -- and I suspect that at least some of the encouragement makes its way back to Henry the same day. Given that he readily speaks on Eleanor's behalf in chapter 12, they seem to be in fairly close cooperation.

Chapter 10/Thursday. She comes with a bozo attached. Discouraging. A loose analogy is having a fly crawling on one's face and not shooing it away.