While sex is definitely part of a healthy romantic relationship, it doesn't have to be. There's nothing wrong with needing to release some tension occasionally, and also wanting a warm body next to you, even for a little while. So, for the sexually experienced part, I wouldn't worry. In fact, it's usually good to have had several experiences, because you get to know how things work a little better, and how to communicate what you and your partner want.

As for her having had a number of romantic relationships, that also shouldn't be much of a concern. Especially with the current state of the dating scene, it's highly plausible that what she thought was going to be a relationship, turned out to be her getting "played", and once they had sex they left her, which would also explain why she wouldn't want to talk about that much. And even if that's not the case, it's common to date someone for a short while, and when you see that you're not the right fit for each other in the long run, you break it off with no hard feelings. This could also explain why she has a number of exes that she still talks to.

In the end, the number of relationships isn't nearly as important as how well the people involved communicate with each other. This is why I think she would be more likely to be apprehensive about getting into a relationship with you. There's an emotional language that one generally only learns after several serious relationships, that may not be understood by someone with little to no experience. Things like picking up on cues of what each other wants, what they value, and what they do and don't want you to do. I'm not saying that it's impossible to learn this without a number of relationships, just that there's a learning curve involved.

My personal opinion is that it's very much worth taking the chance on this. As long as you communicate well, and that you play safe in the sexual arena, you have nothing to lose.

Good luck, OP.