Why is Mrs. Sappleton bored with Mr. Nuttel?
Mrs. Sappleton's boredom is not a function of her character but of the character of Framton Nuttel. It is his fault that she is bored, not hers.
Mrs. Sappleton is bored with Nuttel because of his personality. He is a self-centered person who is not at all good in social situations. We have seen this from the very beginning of the story, where he is unable to think of anything to say to Vera. We then see it again when Mrs. Sappleton is talking to Nuttel late in the story. There, we are told that Framton
... laboured under the tolerably widespread delusion that total strangers and chance acquaintances are hungry for the least detail of one's ailments and infirmities, their cause and cure.
This shows us that Framton does not have the sort of personality that tends to interest people. He talks about boring details of his health that would not really matter to other people, particularly those whom he has just met. It is for this reason that Mrs. Sappleton is bored with him, though she is gracious and polite enough not to let her boredom show.