Your girlfriend has a problem. Her experience is hers and her reactions are hers. There's not a whole lot you can do for her besides being the nice, loving, trusting/trustful sensitive guy you are :-)

You do not want to, for your mental health and that of the relationship, change yourself and your "path" to solve her problem. She has to solve her life's problem, you don't have a problem. If you take on her problem, that takes away from her, rather than gives to her; she becomes "weaker" as a person in her own right.

I would suggest to her that she may want to find a counselor to talk to about her past experience with the other guy or maybe the two of you might want to talk to one together. Her instincts of not saying anything to you when you go out is good but doesn't work on her own "worries" and projection of her past experience on her present situation. She needs to disarm her own triggers.

You do not go out a lot without her or talk to women at the drop of a hat :-) I don't see your behaviors as being anything at all out of the "ordinary". I think you need to insist she work on her problem because, it's obviously already warping you and your thoughts and behaviors and, were you two to break up, you'd have problems like hers but with the next woman who was even "slightly" jealous or worried about cheating. Her anxieties are spilling over onto you and that you can't "solve" them, can't "prove" you are not like that other guy is making you feel like Don Quixote tilting at windmills.

Cheating doesn't enter my mind in reference to my husband. I think I could find him clothed, laying on a bed with another woman and know there was no cheating going on but something else, important to my husband and I would respect whatever it was he was doing. I have no doubt were the situation reversed, my husband would listen to what I had to say too and not "fly off the handle" suspecting something else. Cheating would not be the first thing either of us worried about.

You can't help your girlfriend's trust because you are not/have not been untrustworthy, a memory of her past has been and you can't "fight" that ghost for her because it is not now, is not "real". Urge her to get help for her personal insecurities instead of just trying to "understand" her because they affect you and the relationship too. It's not a case of the parent looking in closet and under the bed to convince the child there is no monster, leaving the night light on, etc. but the parent not being "involved"/dragged into it because the parent is 110% sure there are no monsters. With feelings like cheating and that her ex- did it; it's not so easy to feel, "Well, this other guy did it, maybe I'm capable of doing it to and just don't know it?" or, "I'll just make sure I never talk to another woman every again and everything will be fine" when that's not possible and limits YOUR life, doesn't really fix her problem.