Shalom kvod ha rav.
45 years ago I broked an advanced relation with a woman short before chatuna.No vort was done yet.
Afterwards both built happy families.
Do I have to ask for forgiveness?
It is hard to give a definitive answer without knowing the specifics of why the engagement was broken, etc. In general though, yes you should ask her mechila, even though it is a long time since then, because she had a lot of embarrassment, and emotional pain because of it. Although she remarried, that does not necessarily take away the pain and suffering the she underwent. Additionally, the minhag is that the mechila should be written that she is mochel with a whole heart and that she has no more claims against you. It is very possible that after such a long time, she will be mochel easily, nevertheless she should be placated, in order to attain her mechila. Such a situation is very difficult, and it might be better to have a third party talk to her about it, in order to make things easier.
Teshuvos Vhanhagos 1-735, 2-621, 622, Mishne Halachos 17-128, Kol Hatorah 70 pg. 315.