The beauty, who accepted her boyfriend Jon Shook's proposal last summer (12), stars in the Emmy Award-winning drama as Natalia, who is set up on a blind date with Driver's character Adam Sackler.
Appleby reveals they instantly clicked on the show's set upon discovering they were each in the midst of wedding planning.
She tells New York Magazine, "I met him on set one day, and I was kind of like a fan going, 'Oh my God, there he is!'
"We got along really, really well. He's just a really nice guy. He's focused on the job and he didn't seem weird or creepy to me (like his character). He was just a gentleman. Like the first day we were working together, he knocked on my trailer door and he came in and was like, 'I hear you're engaged.' I was like, 'Yeah, I am.' He's like, 'So am I.' It was just kind of very easy and he made me feel really safe."
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