"He said, 'Buy yourself an electric piano, and I'll take you on the road with me.' And he said, 'I'll pay you what the band's getting,'" Dees said during the NPR interview, which is posted on his Dees' website.
He went on to tour Europe and perform on the Ed Sullivan Show with Orbison, with whom he also co-wrote numerous other songs, including "It's Over," which also was a No. 1 hit.
The Texas native left home to seek work in Nashville, Tenn., where he went on to write songs recorded by performers who also included Glen Campbell. But working with Orbison defined his career.
Dees became embroiled in a lawsuit over "Oh, Pretty Woman" that made its way to the U.S. Supreme Court in the early 1990s, after rap group 2 Live Crew recorded a rewrite despite being refused permission by Acuff-Rose Music Inc., which owned the copyright.
Dees, who detested the ribald rewrite, explained: "It's like if someone asks you if they could use the car," he told The Associated Press in 1993. "We said no, but they take it and paint it all different colors."
The high court sided with the raunchy rappers, saying the recording was a parody that could be considered fair use. Both sides later settled.
Dees eventually moved with his family to Arkansas, and he lived in the Ozarks region of northern Arkansas and southern Missouri for more than 20 years.
A memorial is planned Saturday in Mountain Home, the northern Arkansas city where he died on Oct. 24, according to the Kirby and Family funeral home, which didn't release details about his death. Another gathering will be held next month in Branson, Mo., home to the late Andy Williams' famous Moore River Theater.
Dees said in a 1970 interview with the Amarillo Globe-News that he first met Orbison when he performed in Amarillo, Texas. Dees went to Nashville twice in 1962 to work with Orbison, then decided to move his family there in 1964, traveling in a 1955 Pontiac.
"My wife and I decided that we would go as far as the car would take us," Dees told the newspaper. "If it broke down before we got there, we would save money and move further on later."
They made it to Nashville, where the car soon broke down — and Dees said he had to use his overcoat as payment to get the car towed to a mechanic, the newspaper reported Wednesday.
Dees didn't initially seek out Orbison after moving to Nashville because he wanted to establish himself without help, according to a biography on Dees' website. But the pair reconnected, and with Orbison, Dees crossed Europe and twice went to England.
"I was shocked when we got off the plane in London, and there was like 10,000 people there at the airport meeting the plane," Dees told NPR. "It was like The Beatles when they came over here."
They appeared with The Beatles and the Rolling Stones, and played on the Ed Sullivan Show.
Dees continued to write songs and perform, and released his first solo album in 2002, "Saturday Night at the Movies," which includes songs he wrote with Orbison.
As a child, Dees lived with his family in Borger, Texas, where his father worked as a sand and gravel supplier, where Dees went on to work. Dees recalled listening to barrelhouse piano music at house parties and getting bit by the music bug, according to his biography.
Dees said many times that he and Orbison were life-long friends. Orbison died in 1988.
Dees is survived by his wife, Nancy Decker-Dees of Kissee Mills, Mo.; four children and two step-children, a brother and numerous grandchildren and great-grandchildren, according to the funeral home's obituary.