You need to take this matter up with YOUR MAN!
I'm sorry but unless this girl is Single White Female, she has to be getting some type of encouragement from your boyfriend to even feel comfortable sending him texts like this. You stated that "He told her he \has his good days with me and his bad days."
So what is really going on? Does he have some type of friend relationship with her? Does he talk bad about you to her? If so that has to stop. Hun watch your boyfriend because I have a feeling there is more to the story then he wants you to know. If he told you that he said that, think about the other stuff he probably said to this girl that he didn't tell you. Not to scare you, but we have to be realistic. It sounds like there is a possible affair going on.
The girl already has a problem with you for the simple fact that you are dating him so anyway you confront her, you are not gonna resolve anything. She's not gonna back off just because you said so.
If your boyfriend didn't want her contacting him, she would stop. Or he'd ask her to stop. Or he'd block her number, tell her to leave him alone, ignore her texts, tell her to respect your relationship, tell her that he is with you and that's all that matters...there are a whole lot of things HE could be doing. He is the one who knows this girl and talks to her all the time so he should address it.