The advantage of a mundane bildungsroman is that the mundane setting lets you draw in events from their own intrinsic realism. To Kill A Mockingbird could have the shooting of a probably rabid dog because such things happen. (You note the looser weave of the plot helps there. The dog was not foreshadowed, did not indicate someone unleashing it on them for malice, and did not carry forward; Atticus's shooting skills were not set up for another use, the dog's owner did not pledge revenge or even act with carelessness and folly that this foreshadowed. It merely indicated a milestone in Scout's moral development. Though judicious reading often discerns a lot more cause and effect that are evident at first.)
The quest, or other such fantasy plot structure, chains the events together in cause and effect. Whatever the central problem is, the events relate to it.
A fantasy bildungsroman has neither, which may help explain why they are rare except as half of a quest or the like.
Which is why I was glaring at the outline thinking that they needed something to happen in the winter time, and not the sort of study and practice they've been doing all along. Well, not unless it backfired badly, once. Or a dance of some kind. Or someone willfully making mischief -- but not too much mischief, so I can escalate later.
Then I considered the events of the springtime, and realized that Vera could leave them there alone. Which a certain other character would deem a perfect opening.
On the other hand, it reveals that the characters are not yet fully developed. Of the seven students, I knew what two of them would say in response to being alone, in mischievous suggestions about what they could do wrong with her away. Mind you, they don't mean them, but every one should have a different one, in character. Loveday, of course, would suggest being good at the end, and Arianna proposes using up the sugar, but for the other five, I would think up something and not know which of them suggested it.