Proud
Sometimes she coaxes him outside, on those rare occasions when they happen to be in the manor at the same time.
She sometimes thinks that it only happens because he made a mistake- maybe he forgot that she would be there at that time, was distracted by his subordinates or some important duty or other. Except that Byakuya doesn't make mistakes.
He follows her silently; stride light and graceful, eyes dark and heavy. Usually he asks her how she is progressing, and she dutifully reports that she is doing fairly well. She always wishes she could tell him something wonderful, something amazing, something that would shock him out of his perpetual composure and make him feel something for her.
Pride.
She wishes he was proud of her.