You are both right. This is one of those areas where there is no clear “right” and “wrong”. It sounds like you were not deliberately dishonest with your girlfriend. You didn’t intentionally withhold information from her; you just thought it was truly unimportant, especially since there was no further issue beyond the initial invitation. You handled it with integrity and the situation was completely resolved.
From your girlfriend’s perspective, there is a woman in your immediate environment that you interact with everyday and she has shown a clear interest in you that is more than co-worker sociability or friendliness. It her mind, it is relevant information, even if nothing came of it. She probably wants to know because the attraction, if taken further, has the potential to threaten your relationship. Her reaction probably reveals a degree of insecurity and even if you have done nothing wrong, it is important to take her feelings into account in some way.
Neither of you is wrong. But how do you proceed in the future? It makes sense to move forward in a way that honors both of your feelings and preferences. If you are willing, it could be helpful to agree to share incidents like this with her in the future. On the other hand, you could let her know that you would prefer not to be informed (or that you don’t care either way) if she should encounter this type of situation—unless it poses a real threat to the relationship. It’s OK if you ask for different things.
However, if honesty and direct reassurance are not enough for your girlfriend in situations like these, there is a deeper issue of trust that needs attention in your relationship. In order to deal effectively with that larger issue, you will have to talk it through with each other on your own. If you get stuck in those conversations, you always have the option of seeking help to work through these trust issues.