When Derek Shepard and Meredith Grey broke up, he started dating again, but no one really thought he'd be happy with anyone else. Until Rose showed up. When they get together, she has evidently worked with him on 36 of his surgeries when he finally noticed her. She seems to be everything he's looking for in a woman. They are taking things slow and didn't sleep with each other right away. She's completely in love with him. Derek seems to like her okay, too, but when they finally sleep together, he admits that he thought about Meredith the entire time. Things are a little rocky for Derek and Rose the day after, but he tells her he wants things to be fun and light.  She stays with him, but more and more, she realizes that Derek and Meredith are inevitably in love still.  Eventually Derek realizes this, too and breaks up with Rose to be with Meredith.  Though Rose takes it well at first, she starts to show some hostility towards Derek in the O.R.  Derek realizes they must break up "professionally."  Rose fights it and tells Derek she isn't going anywhere, but when her hothead leads to cutting Derek's hand in the middle of surgery, she realizes she can't afford to make mistakes like that (she handed the scalpel the wrong way).  She leaves to work in neonatal surgery.

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Season 5: 

Meredith's Cold Feet (episode 1)

Season 4:

"Fairy Tale" Love (episode 15) 

The "Sex Survey" (episode 14)

Gettin' Busy. . . or Not (episode 13)

Derek and Meredith Apart (episode 12)

Derek Shepard and Nurse Rose Have a Moment (episode 10)

Derek Shepard Back on the Dating Circuit (episode 8)