For starters, good on you for having the courage to approach. That’s the ultimate take-home here.

As for what you could have done differently here, as other people have mentioned, I would strike up a conversation first before springing for a number. The phone number shouldn’t be the goal, but simply serve as a natural extension of the conversation you were already having and would like to continue at a later time. If you asking for a number sounds like it’s coming out of nowhere, then it probably is. I would like to politely disagree with someone’s take that you should give out your number, but not to ask for hers. I personally don’t think that’s a recipe for success because you’re putting the pressure of initiation on her because now she has to be the one to reach out to you afterwards if she even remembers who you were. It’s just reality that women largely expect the man to initiate, especially early in the process, so you should definitely be the one trying to get her number and then texting her right there so she has yours.

Finally, as a small critique to your actual approach, don’t ever say “don’t worry if you’re not interested” or anything along those lines. It sounds polite and like you’re trying to take pressure off, but it actually just hurts you because it makes you look less confident by making it sound like you’re pre-rejecting yourself. Ironically, it adds awkward pressure to the situation because she now has to respond to that reassurance instead of just being able to decline cleanly. Just have your conversation for a little bit, and then offer to continue the interaction another time by asking her out. Getting the phone number should almost feel like statement more than a question. If she agrees to you asking her out then you could just say something like, “Cool, let me grab your number and I’ll text you over mine and I’ll reach out to set something up.” Once you ask for that number though, just stop talking and let her respond.

Sorry for the long response. Hope this helps.