O'Donnell said Wednesday it took nearly two years of requests, including a meeting with the crown prince at the Saudi embassy in the United States, before he agreed to the interview.
"They want the world to see them in a different light than perhaps the world's perceptions are," she said.
The 32-year-old leader of a key Middle Eastern ally of the United States has taken steps to modernize his conservative country since becoming heir apparent to King Salman. Bin Salman, who is visiting Britain this week, begins a trip to the United States on March 20.
Among the changes he has brought is allowing women to drive. O'Donnell said she visited a university where women are training for careers in medicine and are also offered driver's education courses; Bin Salman realizes that some of the contradictions of his country couldn't be sustained, she said.
"The kingdom is at a crossroads," said O'Donnell, who had been missing from her post as a "CBS This Morning" anchor for a week while pursuing the story. "Eighty percent of the population is under the age of 40. They can't continue to be a country that lives off its oil wealth, either politically or culturally."
During his visit to Britain, the crown prince has also faced demonstrators against a Saudi-led war in Yemen against rebels supported by Iran. Critics say the modernization comes despite continued human rights abuses in Saudi Arabia. The young leader consolidated his power by holding rivals and some Saudi leaders captive last fall in a luxury hotel.
It's the first interview of a Saudi leader on U.S. television since one conducted by Barbara Walters in 2005, O'Donnell said. She was making her first visit to the country and her experience illustrated some of the changes in the country where, until recently, women in public had been required to cover their heads. She did not.
O'Donnell said there were no restrictions placed on the interview, which lasted 90 minutes. Her story will air on "60 Minutes" on March 18.
"It's really one of the most fascinating interviews I've ever done," she said.
Another television morning show host, NBC's Megyn Kelly, has a network special this Friday with her interview with Russian President Vladimir Putin. Kelly spoke to him at the Kremlin and in Kaliningrad, her second interview with Putin in the past year.
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