“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.”
“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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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.