I dont understand anyone who wants to get back in contact with a person who cheated on them, betrayed them and never tried to contact you since.
One harsh lesson I have learnt over the years is that women ALWAYS do something they really want to do. If she wanted to contact you, she would have. If a girl really wants something they go after it, even the shy ones. Men would happily have strong feelings for an ex but never contact them because of self-pride etc....
The old saying is true....."if you love someone, let them go, if they come back to you then they must love you too"
I have tried several times in the past to get a gf back and lost my self dignity, but you know what, it never once worked, the only one I ever got back was the one I completely ignored and forgot about.
Trying to be friends with her now will just cause problems for her current partner.