I get where your girlfriend's insecurities are coming from. My girlfriend and her ex-bf are still very good friends as well. At first I found it a little weird, I still get a strange feeling sometimes when I think about how they've been together for so long and how much they have shared that I'm not a part of. But I've accepted it. I know for a fact that they are definitely done as a couple and I don't mind them being friends. We even went out together a couple times and I actually like him.
Still I had to get used to the concept. I guess your girlfriend is in a similar situation, with the added difficulty that you seem to identify as bi (I hope I've gotten that right), you two haven't been together for long and already you hang out with your ex who you are obviously still very fond of. I think no matter how many times you tell her he doesn't stir feelings in you anymore she will always doubt it. She's a girl after all.
It might help if you gave her the chance to be part of your friendship, at least let her get to know him so she will see that he's no threat to her. Although with the distance between you that might be difficult.
I understand you really care about your ex still but maybe you should take it a few steps back with him for the sake of making your girlfriend feel a bit safer. Or, maybe not the best solution, don't tell her you meet him. She won't find out and if there's really nothing to fear for her it might be better not to make her worry.