I would be careful on this issue. When you are dating, I'm imagining that you have some idea that you are dating in an effort to promote from dating to GF to wife.
Women and guns is a tricky subject. Frankly, I would avoid the subject during the early dating phase, because it is a waste of your time to discuss and she may start a texting rampage which let's everyone in 5 states know you are CCW'ing right NOW!
When you are thinking Date to GF, I would broach the subject and even suggest you go shooting together. If the answer is a flat no, I would suggest you move on or at least don't promote. If there is some opportunity to figure out why, that would be good. I find women in general to be relatively gun unfamiliar. I think this is a society problem. Girls often get left out of shooting fun as children and never try it because it feels like a forbidden pastime. When you offer, it should break through those barriers.
At the GF to wife promo, get this right. Guns can be a regular marriage argument, if you go not. I've met plenty of women open to the idea of shooting. You can meet a shooter. It is hard to promo to wife someone who will not partake in shooting with you. If you do, expect 30 years of arguments about purchases, reloading, strange smells, why are you carrying again and other BS.
My wife is just starting to come around to CCW being normal, but she still targets buying guns as a waste of money in our household. It would be sooooo much better if we saw eye to eye on this. I just took crap for joining the range and asking the kids to shoot on youth day at the range!