That's right: she was at Bevendean. It wouldn't surprise me if there was a connection, as you say, it's not very far away.
I do love the ways that old names do keep cropping up when one starts looking into Sussex history.
Great story. I'd never heard of him before. I was at primary school with a Geraldine Dudeney, wonder if she was a descendant.
I imagine any books would have been donated to the school or Mechanics Institute.