Theory:

She broke off with a little shudder. It was a relief to Framton when the aunt bustled into the room with a whirl of apologies for being late in making her appearance.

“I hope Vera has been amusing you?” she said.

“She has been very interesting,” said Framton.
Explanation:
 
As Section II of "The Open Window" commences, Vera's ends her narration- with a shudder. The mere thought of dead people creeping through the window was so scary that she couldn't continue herself anymore. It is also interesting to note that this marks the end of her conversation with Mr Nuttel.
 
Soon after Vera's story, Mrs Sappleton makes an entry. The narrator describes how she bustled into the room where Nuttel and Vera were seated. She was apologising for having made a late appearance.
 
One might wonder why Mrs Sappleton had kept her guest waiting. In this modern age, the behaviour might suggest that the host was impolite and disrespectful. However, one shouldn't come to such conclusions with Mrs Sappleton. As the story was written in \(1914\), it was customary for the ladies of the age to get properly dressed before hosting a guest. Being inadequately dressed was rather considered as impolite and improper. Moreover, getting dressed was a time-consuming task in that bygone era.
If you are curious, you may check out how a lady used to dress during the Edwardian era (\(1901\) - \(1910\)) here. Note the layers of clothes and detailing that goes into getting dressed. Moreover, there is a hairdo and makeup. Those were again another set of tedious tasks.

While speaking of Edwardian customs, it is important to see how Saki had painted the practices of Upper-class Edwardian society in the story. To begin with, we see how Framton Nutttel carries a letter of introduction from his sister. It was a common practice among the upper class of the age. It was often used as an act of ice-breaking tool while meeting people in a new community. Also, we are aware that the story “The Open window” takes place in a country. However, several details from the story reveal that it was set in an upper-class family. Vera’s story shows that the men of the house died while they were hunting. Back then, hunting was a sport reserved only for the wealthy. We are also aware of how Mr Nuttel was encouraged to seek refuge in the country due to an undisclosed nervous disease. Back then, when modern medicine and psychological treatment were yet to be seen, relaxing in the country was a common way of treatment among the English. It was believed that a slower pace of life, fresh air, and silence helped cure individuals suffering from nervous disorders. Unfortunately, such leisure was again reserved for and afforded by the privileged.
So, coming back to the story, it is perfectly understandable why Framton Nuttel never felt offended or impatient while he was waiting. On the other hand, he felt relieved when he saw Mrs Sappleton enter, and that could be because of the story narrated by Vera. He was considerably shaken and disturbed by the tragic story. Mrs Sappleton's entry gave them a diversion, and it also meant that he could get started with his formal introduction and polite exchanges and leave the place sooner.
 
Soon after her entry, Mrs Sappleton addresses Mr Nuttel and expresses her hope that Vera had been keeping him engaged. She asks, “I hope Vera has been amusing you?” to which Mr Nuttel agrees and states, “She has been very interesting".
 
The line "I hope Vera has been amusing you?" is similar to phrases such as "How are you?", "How's it going?", or "What's up?", and hence, can be considered as a way of greeting. Likewise, Framton Nuttel's response was also customary. People tend to respond to such greetings with a positive answer.
 
However, Nuttel's response can be further analysed. Vera had kept him engaged through a gruesome story. As a result, though he claimed that Vera had been very interesting, he hoped that it wasn't the case. Considering his nervous condition, he would have rather spent his time being bored than having listened to Vera's fearful narrative. Hence, the statement is ironic.
 
Nevertheless, the statement can also be considered paradoxical because the meaning is ambiguous (no exactly clear). According to the Cambridge dictionary, paradox refers to "a situation or statement that seems impossible or is difficult to understand because it contains two opposite facts or characteristics". Hence, when you look at Mr Nuttel's response, you can see that the statement is both true and untrue. It is true because Vera had indeed been engaging. And it is untrue because Mr Nuttel felt tortured rather than amused by the story.
 
When speaking of Mrs Sappleton, it is interesting to note that she has a peculiar characterisation. Unlike the other two major characters, Mrs Sappleton (as a character of the story) was so far understood only through what Vera and Mr Nuttel had to say and perceive, respectively.  Despite having been at the centre of the plot of "The Open Window”, she had been physically absent until now. Moreover, this absence of hers had been utilised by Vera to construct and narrate a story on her. Hence, Mrs Sappleton's entry to the story is twofold: the first aspect refers to Mrs Sappleton as a character. Following Vera’s tragic story of her aunt, the readers are finally presented with the character herself. The second aspect refers to Mrs Sappleton as a person in the story. The main purpose of Framton Nuttel's visit was to meet Mrs Sappleton, to whom his sister had addressed the letter of introduction. So her entry gave an end to his waiting and also fulfilled the purpose of his visit. 
 
Despite all the observations and insights, a question remains to be answered. If you had observed, the aunt was completely unaware of what had taken place between Vera and Mr Nuttel. The reason is that Vera ended her narrative before Mrs Sappleton entered the room. So, the question is, was it a coincidence that the aunt appeared after Vera had ended the story. Or was it a conscious effort from Vera's side to finish it before her aunt arrived? If it was the latter, what could be the reason? Could it be that she didn't want to upset her aunt by reminding her of the tragedy? Or, could the reason be something else?
 
Meanings of difficult words:
 
S.No
Words
Meanings
1
ShudderTo shake suddenly with very small movements because of a very unpleasant thought or feeling
2
BustleTo do things in a hurried and busy way
3
WhirlA rapid and frantic activity
Reference:
National Council of Educational Research and Training (2008). The Open Window – Saki (pp. 55 - 61). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.