Hambro, a great-granddaughter of Sir Winston Churchill, said she has been "completely horrified" by the revelations about the financier's conduct and her "heart breaks for all the survivors".
The now married mother of four said she did not suffer or witness any abuse, but added that she hopes those who were raped and molested "get the justice they so deserve".
Hambro, now 44, issued a statement after the logs, released as part of court proceedings, revealed she flew on Epstein's Gulfstream jet following visits to his ranch in New Mexico and Little St James.
At the point she made the trips in 1999, Hambro was a 23-year-old employee at Christie's auction house in New York.
One was a "work trip" to help Epstein decide what art he wanted to buy for his ranch, while another was a "personal invitation" to Little St James.
The island, bought by the former Wall Street financier for just under £5 million, is at the centre of appalling allegations of abuse by Epstein, who killed himself in jail a year ago. Epstein would ferry his victims around the world on his jets.
Records show Epstein, then eight years before his conviction, was with Hambro on both flights, and that his alleged madam, British socialite Ghislaine Maxwell, 58, was also present for one trip.
Writer Hambro's contact details were also listed in the disgraced tycoon's infamous "little black book". As a 5-year-old she was the youngest bridesmaid at the wedding of Lady Diana Spencer and Prince Charles in July 1981.
The flight logs unearthed by the Mail reveal that on February 21, 1999, Hambro flew with Epstein, Maxwell and two other women from Santa Fe, where Epstein had his "Zorro Ranch", to New York's Teterboro airport.
A month later, on March 21, she was on his jet from St Thomas, used by Epstein to access Little St James, to Teterboro. With her were Epstein and two women including a New York socialite.
In a statement last night, Hambro said: "The first flight was a work trip with female colleagues to look at Epstein's new home in Santa Fe to discuss what art he was going to buy.
"The second trip, to Little St James, was a personal invitation, which I thought would be fun to accept, but I didn't know anyone there, didn't really enjoy myself, and never went back. My heart breaks for all the survivors, now I know what happened on that island.
"In the course of those two trips, I was not abused, nor did I see anyone abused, or anything untoward happen, with minors or otherwise. I have been completely horrified about the revelations of his conduct since then. I was clearly very lucky, my heart goes out to those who were abused by him, and I trust they get the justice they so deserve."
She added: "I was young and naive, and could not conceive of what was to unfold." She only travelled on Epstein's jet, logs show, when leaving his homes. It is not known how she arrived.
In 2015, Hambro, now married to barrister Orlando Fraser QC, wrote movingly in the Mail of the day she was Diana's bridesmaid.
She said: "Like Charlie in his Chocolate Factory, I'd won the golden ticket."
Maxwell is awaiting trial for helping Epstein in his abuse. She denies all the allegations.