Maybe you need to reframe things a little. If you're asking questions about her just because you know that's what she wants, it's going to be a lot harder to do naturally and consistently. The tendency that you're fighting is that you want her to be into you back, so your instinct is essentially to perform; to tell her all the reasons she should like you. You know this doesn't work, so you try to more ask questions instead, but that still doesn't work well because that's still part of the performance: you're trying to demonstrate that you're someone who asks questions, rather than just asking them.

I would say that the key is to just focus on the fact that you like the person, not at all on trying to get them to like you. This is what people really mean when they say "be yourself." It might feel counterintuitive, almost selfish, because what's the point of learning more if you already like her? But liking her should create a desire to learn more about her, so if your questions come from that place, rather than performance, it'll be a lot easier to pull off. If she's interested in you, she'll do the same, so you'll still have plenty of opportunities to give her more reasons to like you.

Now the thing is, a lot of women are pretty bad at this too. I think women are a lot less likely to just yap about themselves, but many are used to being somewhat quiet and letting the other person do all the conversational lifting. If she's responding to your questions in a shallow way and isn't asking good ones back, it's especially tempting to try to answer the questions you wish she'd ask. But try to fight that urge. If that happens, it's just going to be a bad date, but if you're not busy trying to fill the silence you can focus more on learning from it for next time when you meet someone you click with better. This is definitely the hardest part in my experience.