Great job moving outside your comfort zone on the women you're getting to know... that's hands down the fastest way to improve (so long as you hang in there through those early ups and downs).
The ounce of prevention here is asking her for her schedule first: "Let's grab a bite or a drink sometime this week or next," when you ask for her number, and, "When's good for you to grab that bite or drink?" when you text her to set up logistics. Then you don't run the risk of proposing something and her having to say "no" because she already has plans.
Good rule of thumb: don't ask her out EVERY time you see / talk to her, but every other time is fine. So, next time you see her, make some small chit-chat, don't get too involved. The next time you see her after THAT, even if you have to chase her down to talk to her, just grab her and tell her you need to go grab an ice cream sometime and discuss Disney films and politics (or whatever humorous callback you can come up with that works with your prior conversations with her), then grab her number so you can sort out logistics.
If she likes you, she won't say "no" to ice cream, Disney flicks, and politics!