Most Helpful Guy
Relationships are not equal, love itself isn't. For a sexual relationship to work the Man have to have the hand, because we Men are the responsible for everything that happens in our relationships, intended or not intended. You being dumped puts you in a lower, weak position, you didn't have the hand. You were more invested in the relationship than her, you were the disposable side, the one needed the least. It simply wasn't your relationship, it was hers, and because she thinks it's still hers she might want to do this kind of things, or may be worse, who knows. You not wanting to get back together does naturally come as a surprise to her, you're supposed to be the one who needs the other more, right?
Here's my advice. A girl dumping you is bad, you cannot get back together unless you claim the hand in the relationship. The only way you could get back in under your OWN terms. Your relationship, your rules. She can take it or leave it. You're wise, honest, and respectful, but you're not an stupid idiot. You're not forcing things, you're just inviting her to join you.
An alternative advice. Move on, find and date other girls. There are no special girls out there waiting for us. The myth of the One is so pathetic it makes me sick. If she wants to get back, you could keep her around as a booty call, or FWB. Committed relationship with her? Why bother, it didn't work the last time, there's no point in trying a second, third, fourth, time.