A lot of good points made... maybe a couple more:
Don't defend your viewpoint. Make her defend hers.
First, talk about the fundamental logical error that many make. They see that X% of homicides and Y% of suicides involve a firearm, and assume that if firearms were eliminated, that percent of the homicides and suicides would go away. The best evidence is that they would not. People simply find other means. Japan is practically gun free, but their suicide rate is twice ours. Obviously, they are coping quite well with their lack of firearms. Malaysia has practically no private firearm ownership, and their homicide rate is about the same as my home state, Utah, which is practically awash with firearms. As nearly as anyone can tell, if you eliminated all the firearms in the US, it would have no good effect on crime rates. More than likely, it would make things measurably worse. It's not the firearms that are the problem. It's us. Nobody has yet found a positive correlation between the strictness of gun laws and the homicide rate.
If she's a CPA, talk in terms of balancing risk and reward.
Ask her how many times per year firearms are used wrongfully. Then, point out that by the most conservative estimates they are used more than 10X as often to prevent crime. For every crime committed with a firearm, 10 are prevented with one. If it saves just one life, isn't it worth it to have an armed society?
Criminals are not looking for a fair fight. They want an easy target. 93% of the time, if you show a firearm, your assailant will flee.
If she wakes up in the night and a large, foul-smelling rapist is just entering her bedroom, exactly what's her plan? What's the conversation to occupy the three minutes or so that it takes a good police department to respond? Those minutes tend to be violent and ugly.
I know what my wife would do. She'd put two rounds in his center of mass so fast it would make your head spin. That's the choice she has already made.