Alyce shows personal growth throughout the entire book. For me though, there is one specific location where I see significant growth for Alyce.
The time is when Alyce actually takes on the name Alyce. Jane has been injured, and she is not capable of going to the Saint Swithin's Day Fair to buy supplies. Alyce goes instead, but at this point in the story, her name is Beetle. Jane originally found Alyce sleeping on a pile of dung and decided to call the girl Beetle. While at the fair, somebody mistakes Beetle for somebody else. He calls her Alyce, and Beetle decides to take the name as her own because she likes it. The change in name is symbolic of Alyce's growing confidence. She no longer feels like the girl found on a pile of poop. She is gaining confidence in herself, her education, and her skill set, and Alyce feels that "Beetle" doesn't fit with who she is becoming.
What a day! She had been winked at, complimented, given a gift, and now mistaken for the mysterious Alyce who could read. Did she then look like someone who could read? She leaned over and watched her face in the water again. "This face," she said, "could belong to someone who can read. And has curls. And could have a lover before nightfall."
From this point in the story, Alyce begins showing a great deal of confidence in herself. Sure, she still makes mistakes, but this new confidence is what allows her to continue working hard for personal improvement. Beetle would not have returned to Jane at the end of the story to get her job back. Alyce would though, and she did.