The first time she meets Sarah-Jane Smith, Rose Tyler is not jealous at all.
She's worried, of course, because the Doctor doesn't talk about Sarah-Jane, or any of his old companions, actually.
She knows they existed, that much is obvious by going through the wardrobes, but she knows absolutely inothing/i about them.
Really, she know's absolutely nothing about him.
The first time she meets Martha Jones, Rose Tyler is not jealous at all.
She's sympathetic, if anything, because Martha is so much like her when she first met him. She's amazed by him.
And, the only real difference between the two, if she's perfectly honest with herself, is that Rose met him first, Rose had that.. that.. thing with him first.
Really, her thing with him could of happened with anyone.
The first time she meets Donna Noble, Rose Tyler is amazingly jealous.
Not of Donna, though, she's not jealous of Donna's relationship with the Doctor, she's not jealous of the just mates, of the molto bene!, of the need to impress.
She's jealous of the Doctor's relationship with Donna, she's jealous of the relationship assumptions, of the watch it, spaceman!, of the want to be impressed.
Really, she wishes she knew this fantastic woman.