"We'll probably avoid that for as long as possible," Rachel Bilson tells PEOPLE of introducing her daughter to Hayden Christensen's onscreen personas

By Lindsay Kimble
June 16, 2017 02:15 PM
Credit: Michael Buckner/Getty

Rachel Bilson and Hayden Christensen‘s daughter is still too young to understand what Mom and Dad do – and the actress hopes to keep it that way for a while.

“We’ll probably avoid that for as long as possible,” Bilson, 35, tells PEOPLE in this week’s issue of introducing Briar Rose, 2½, to her and partner Christensen’s onscreen personas. “Especially because her dad is who he is.”

Christensen, 36, famously portrayed Anakin Skywalker – a.k.a. (spoiler alert!) Darth Vader – in Star Wars: Episode II – Attack of the Clones and Star Wars: Episode III – Revenge of the Sith.

“She might be like, ‘Oh no! Darth Vader’s my dad!’ ” Bilson points out of her daughter, joking, “No one’s gonna mess with her on the playground.”

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The actress is cherishing every moment with her toddler, and admits that “me time” has become a thing of the past.

“My me time is ‘we time’ now,” she says. “It’s always about her. It’s not about lying out and watching a movie anymore. Those days are gone! But I’m happy with the new version.”

The O.C. alum is back on the small screen, though: She recently kicked off a season 5 arc on CMT’s hit drama Nashville.

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Of her character – Highway 65 Records’ new CEO Alyssa Greene – Bilson says, “She’s a fish out of water” who “comes from Silicon Valley, so she knows nothing about country music.”

Though a fan of the series, Bilson confesses she’s “only grazed the top layer of country music.”

And while she’s enjoying her deep dive into the genre, don’t expect the actress to do any onscreen singing. Of the prospect, she admits, “[It’s] terrifying.”

For more from Rachel Bilson, pick up the latest issue of PEOPLE, on newsstands now.