Episode 2x4, Everybody Hates Hugo

Hurley asks Rose why she hasn't asked about the hatch and then takes her there. He asks her not to tell anyone and she says she wouldn't know what to say anyway. She is amazed with the food pantry and helps Hurley take inventory.
Later, she finds Hurley ready to blow up the food and she stops him.

Episode 2x6, Abandoned

Hurley wants to know why Rose is hanging laundry to dry when there is a perfectly good dryer in the hatch.

She says she doesn't want to spoil herself.

Episode 2x8, Collision

Rose tells Jack it's good to see him out of the hatch and gives him some fruit.
Later, she sees Bernard for the first time since the crash as he comes out of the jungle.

Episode 2x16, The Whole Truth

Rose and Bernard argue. They run to Sun when they see she is in pain, but Sun says she's fine. Rose says that Bernard is mad at the world because he forgot Rose's birthday.

Episode 2x19, S.O.S.

Bernard gathers people to help him build an S.O.S. sign in the sand on the beach. Rose thinks it's a bad idea and they argue. She finally tells Bernard that the healer he had taken her to didn't work, but that the island has made her better and she never wants to leave.