Did I screw up, or is it just a mystery?

I recently graduated from college. At my graduation ceremony I met an amazing girl that was seated next to me because our last names were similar and we were both in similar colleges (college of the arts).

We talked for a bit, making friendly conversation and joking about various things throughout the ceremony. Nothing serious. Towards the end I asked her for her number and she gave it to me.

Later that day we talked just for a little bit about where we were from and what we did after the ceremony, and later talked about plans now that we were graduated. All responses thus far had been very positive. No short responses, no massive lags of silence, and general upbeat sentiments.

At this point I asked her out on a date (specifically using the word "date" to avoid any ambiguity), and she asked what I had in mind. I discussed it a little beforehand with some male and female friends, and we all agreed that we didn't like typical dinners and movies, and that something outdoors and casual was a good break-the-ice date, so I suggested bowling or mini golf.

She told me she was good at mini golf but very bad at bowling. No specific yes or no was said. I suggested a day that weekend and she told me she had plans. I tried to reschedule but never got a response back.

Now, I'm not some stuck up dude. I completely understand that someone can just be uninterested. I get that. So I would have understood not giving me her number. I also understand that sometimes that's uncomfortable too, so I would get if she just never answered my first texts.

But am I right in assuming that asking a girl for her number is generally seen as a romantic attempt? Might she have thought I wanted to be friends? Could she have just lost interest entirely over the course of a few days? Why might that happen? Is there a "too soon" to ask a girl on a date?

I don't often over think things this much, but I'm genuinely curious as to what might have happened, and if it was me, I would like to not do it again.