If you have to do anything or be anyone but (yourself) in order to get her then she is NOT "the one" for you!
All relationships will have their challenges but at the very least they should start off with (both) people wanting to be together.
Having said that it is not uncommon for some people to "romanticize" their past relationships. This is especially true if they did not want their last relationship to end. You can't compete with a ghost!
Depending on her age she may that "bad boy" phase mentality. "We adore those who ignore us and ignore those who adore us." Women in this phase spend more time obsessing over guys that make them feel they have to (earn) their affection and attention. Those guys are seen as a "challenge". There is always an element of drama and mystery because the women don't know where they stand with the "bad boy".
Insecurity gives them butterflies in their stomach. Contrast that with dating a "nice guy" who pours his heart out and answers there every beck and call....etc Women who are in the "bad boy" phase would find "nice guys" to be boring and unexciting. They're "too nice" and do not pose enough of a challenge. In their mind the more abundant a thing is the less value it has. A "bad boy" is stingy with everything! (compliments, affection, and time). Oftentimes when the "bad boy" tosses a few crumbs women are quick to mistake it for the whole cake.
If your girlfriend's ex was a "bad boy" she may not have evolved from that phase yet. Only a rise in self-esteem and being tired of heartache causes women to let go of the "bad boy" as an ideal mate.
All you can do is treat her the best you can and always be loving and sincere with her. No two relationships are alike. A "first love" is often more intense because everything is "new" and we've never experience so many highs and lows before. Eventually with experience and age comes wisdom. At some point we come to realize if they're not with us then they must not be "the one".
What you need to do is (free yourself). You need to stop thinking about her ex and her past. Focus on the fact that she is with you now and make the most of your time together. Your thinking about him will keep you from enjoying what you do have together. In fact it may eventually cause you to lash out her. He's not your ex he's her ex. You shouldn't consume your thoughts with him.
Be grateful that he let her go or else you wouldn't have her.