Molly's mother Elizabeth Kendall was a 24-year-old single mum when she met charming Bundy in a bar.
Falling for Bundy, who appeared to be genuine and caring, Elizabeth shared a home with the vicious killer for seven years.
Molly, who was three when Bundy came into her life, has written a new chapter for a revised edition of her mother's book, The Phantom Prince, which was first published in 1981.
The book was used to inform the Netflix movie Extremely Wicked, Shockingly Evil and Vile, which starred Zac Efron as Bundy and Lily Collins as Elizabeth Kendall.
In the chapter, Molly describes how she thought of Bundy as the father she never had. The murderer, who is believed to have killed up to 100 women, taught Molly how to ride a bike and took her skiing.
But Molly explains she sometimes glimpsed Bundy's dark side.
Once, when the pair were swimming in a lake, Bundy kept pushing a life float away from Molly as she exhaustedly tried to reach it.
On another occasion he crept into her bed, and during a game of hide and seek, young Molly found Bundy naked and aroused.
Although Molly never told her mother about Bundy's sinister actions, Elizabeth had her own fears.
Bundy regularly left the house at night, and after learning that police were looking for a man called Ted who drove a bronze Volkswagen in connection with the murders of two women, Elizabeth reported her suspicions.
Bundy was eventually convicted of three murders, but before he faced execution by electric chair in 1989 he confessed to killing 30 women and girls.
It's believed he could be responsible for dozens more.
The 2020 edition of the Phantom Prince is published by Abrams Press.