"...[A]llow me to conceal carry..."?!
At this time, you're dating -- not married. I understand that the difference here is that you were evidently not necessarily interested in guns when you entered the relationship. However, people - and their interests - do change. And if you're talking about carrying, then this must have become rather important to you for some reason.
The first thing you need to do is determine just how important this is to you, solidify WHY you want to carry in the first place. Once you have that firmly nailed down in your own mind, you need to be able to calmly and rationally present your reasons to your girlfriend. While this is going on, you need to demonstrate your own commitment to this course of action by regularly honing your skills. Now, I'm not talking about flaunting anything here, rather, just quietly going about your business. At this point, this is as much about showing her how important this has become to you as anything else. When she objects, patiently but firmly deal with her objections.
The most important thing you can do is to quietly demonstrate that she can TRUST you to do the right thing with your firearms; her objections may have as much to do with not knowing if she can trust you with firearms as they have to do with her ideological issues. Trust can, in many cases, triumph over ideology. I have been married for nearly 15 years. My wife and I are both comfortable with firearms; I am quite good with them. But the idea of carrying is a recent one that took some time for her to accept, especially around our children (who have no idea at this time that I am carrying). I addressed her concerns over the course of several discussions, and took my CPL course even though I knew she wasn't completely sold on the idea. I wasn't confrontational, I simply explained why this had become important to me, and quietly demonstrated my commitment to carrying. I have also taken her shooting - and she has witnessed my skills first-hand, which gave her even more reason to trust me with carrying. Today, she still isn't 100% sold on the idea of carrying from an ideological standpoint, but she trusts ME and understands WHY I came to my decision to carry. She is now beginning to toy with the idea of taking a CPL class herself, and is even beginning to look at sidearms that she might be able to carry.
It didn't happen overnight. It takes time, patience, understanding, persistence, and commitment to your own ideals. And if your girlfriend decides that she can't live with this aspect of your life, then it is better to find that out NOW, rather than after marrying the girl and having to put up with arguments every time you go to the range or strap on your sidearm.