If it bothers either of you then you risk that it may end up destroying you. Look at how this affects your trust of her right now, and as you're dating how you feel when she has to work late, or cannot see you for some reason.
If you even once doubt her, then the trust is lacking and it will destroy you in the end. Not to offend you, but you seem to have taken this to heart a lot at such an early time, I imagine that you feel like she has cheated on you from what you have written, and that she may well cheat on you.
Only you can decide how comfortable you are. If you can't deal with it, then do not even put yourself in the situation is my advice.

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