The interview is due to be taped Friday.
As it is, Ferguson is already displaying a stiff upper lip, and even a sense of humor, only days after being exposed trying to sell access to her ex-husband, Prince Andrew.
"We all make mistakes," said the Duchess of York, 50, on Wednesday night at a party in New York for the launch of her new line of children's books. "Yet we go on. We dust ourselves down."
Asked by PEOPLE at the event how she is faring, Ferguson replied, "Very good," then added with a smile: "Perhaps 'very' is not the right word.' "
Before the crowd, Ferguson immediately broke the ice by referring to one of her titles, Ashley Learns About Strangers, and quipping, "Perhaps I should have taken a leaf out of my own book." When the remark received a muted response, she smiled broadly and said, "Where's your sense of humor tonight?" That delivered a big laugh.
She thanked her publisher, Sterling Publishing, and those who attended the private party. "I think it's important you all came here tonight," she said. "The show must go on."
Ferguson was caught on video taking money from an undercover reporter in exchange for a promise of business access to Prince Andrew, a British trade ambassador. She apologized, calling her actions a "serious lapse in judgment," and friends have told PEOPLE she is "utterly remorseful and regretful."
The duchess has written a number of children's books. The latest series, aimed at helping kids through difficult moments in life, includes four titles so far: Matthew and the Bullies, Emily's First Day of School, Ashley Learns About Strangers and Michael and His New Baby Brother.
The books go on sale in the U.S. in August.