In "The Story-Teller," what does the bachelor's telling of the "improper story" reveal about the children and their aunt? The children appreciate their aunt's storytelling more than the bachelor's. The aunt's belief that the children will behave better when told good and proper stories is incorrect. The bachelor is a better and more proper influence on the children than their aunt. The aunt's story is more influential on the children than the bachelor's story.

In Saki's short story "The Story-Teller," the bachelor's telling of the "improper story" reveals that the children are more captivated by stories that are unconventional and that challenge the expected moral norms. Contrary to the possible options given, it actually shows that the children appreciate the bachelor's storytelling more than the aunt's. The aunt represents the traditional and didactic approach to child-rearing and storytelling, where stories are meant to impart a clear moral lesson. However, the bachelor's "improper story" is more engaging to the children because it is unpredictable and features a character who is rewarded for her bad behavior rather than being punished.

From the responses of the children and their clear preference for the bachelor's story over the aunt's dry, moralistic tales, it's evident that the children find excitement in narrative elements that break from convention. They are fascinated by the idea that someone who does not follow the strict rules of conduct (like the story's protagonist, Bertha) can not only succeed but also be celebrated. The bachelor's story is more influential on the children than the aunt's story, suggesting that the aunt's belief that good and proper stories will make the children behave better is incorrect. It might be inferred that the bachelor, through his storytelling that defies the norm, is a more appealing and impactful figure to the children than their aunt, at least in the realm of storytelling.