Bebe gave her virginity to Todd, at the age of eighteen. Todd and Bebe had a romantic relationship at first, but after over two years together they decided to have an open relationship. Todd cared for Bebe`s daugther Liv like if she was his real daugther.
She began modeling at the age of 18 and moved from her hometown of Portsmouth, Virginia, to New York City. Shortly after moving to New York, she met rock star Todd Rundgren. At the time she was living in a women`s home run by nuns. Bebe and Todd began dating, moved in together, and ended up living together for six years. Although she and Todd were in a steady relationship, they both dated other people while they were living together.
When Bebe`s daughter Liv Tyler was born in 1977, Rundgren was named as the father. Todd and Bebe broke up around this time, and Bebe moved on to other rock stars such as Stiv Bators of The Dead Boys and Rod Stewart.
When Liv was 11 she found out her father was really Steven Tyler, not Rundgren. Bebe has said in interviews that she didn`t want to tell Liv who her real father was because of Tyler`s severe drug addiction at the time, and she thought he would be an unsuitable father. Rundgren had known that he was not Liv`s biological father but kept the secret in order to give Liv some semblance of a stable home life. When the truth came out, it put a strain on the relationship between Todd and Bebe. However, Liv and Steven were able to form a family bond and are reportedly very close. Liv also changed her last name from Rundgren to Tyler.