I don't know if it's actually a quest or not, it's the romance thing you do with her/him. You know, befriend them, tell them to be awesome, then they love you? (Yeah, I know I missed a few steps, but you get the picture). I'm playing on the public build, so I don't know if that makes a difference, but for some reason I can never get Bess's romance/quest/thing to finish. I've gotten up to her watching the news with me or maybe it was her cleaning up around the ship but I never progressed further then that. I tried using the wiki but nothing came of it. Also, I'm about 150 days or so in so I thought it would've activated by now. Is there something I don't know?