I will speak from experience here. I am an avid shooter/hunter, and since living w/ my wife I wanted to start collecting firearms again since my dad took them all from me after my parents got divorced (guns were family heirlooms from my real father) Wife though had a real hard time dealing with this when I talked to her about it when we went on a nightly walk for exercise, and we got into a heated debate, and it didn't end very well.
Wife's point : A. We don't need one
B. Why spend $xxx.xx on a gun when we don't even spend $xxx.xx on something that we could actually use daily
C. I just don't like them.
My point: A. This would be a possession I would value highly, and I don't have very many things I want/like to collect
B. This could be used to defend our homes, go hunting with, spend bonding time with her father (who is a AVID collector/firearm user)
C. It's only fair if I let her collect/buy expensive things, etc.
So after a while, I went from a Zero gun household to now a 3 gun, I have a Mosin-Nagant (Cheap); S&W K22 revolver (dad gave it back); S&W Sigma .40 cal (for home defense).
Basically, I research my purchase, explain to her what I want to get and make sure I can get her on board that it is a good deal/reasonable purchase, that we can afford it. Then she basically gets to do something nice for herself (like go on vacation w/ her girlfriend, get an IPOD or something) and we are all happy.
This is a very delicate situation, I'm afraid if you just say it's my way or the highway then she will dog you forever about it and it will suck ass, so you got to meet both ways somewhere or sacrifice something (me, I have to spend equal $ on her). Luckily her dad is on my side and she respects her dad like Jesus so it helps me out.
In your situation, you aren't married to the girl so maybe this is a sign you can back out now. If you want a gun, buy one, but just explain clearly why you think its a good idea.
&EDIT& forgot to say, I HAD To purchase a safe in order to store these firearms securely yet also provide reasonable access in the event of a breaking and entry. I am totally fine with this as it is the logical thing to do regardless of whether or not you are by yourself or with children.
Explain to her and show her how nice safes are, and that she can also store her valuables in there as well.