I am not particularly good at picking up on social cues, and, regardless, a question of what cues might indicate the answer to my question would be more opinion-based.
For context, I am an 18-year-old male college student in the United States. She is also 18.
We met a little less than half a year ago during orientation. We talked some, but I was not interested in her at the time. When school started about a month later, I noticed that I was running into her rather frequently, and we got to know each other a bit.
I finally decided to ask her out roughly three months ago. She said that her family would be in town, and, thus, she could not go. Suffice it to say that this was true. Now, what I had been planning for us to attend was a monthly event, and some schedule changes of mine made it far less viable for me to attend in the future. Still unfamiliar with the local area, I could not think of much in the way of a substitute.
I had the same question then as I do now: I was not sure if she would have liked to go in the first place. I did not want to risk being bothersome to her, so I took a cautious approach and did not reschedule. Take this as a sub-question: in such a situation, would it be best to try to reschedule the date?
As the semester intensified, my schedule became more erratic, and I saw her far less often. About a month or so ago, though, she sent me a text out of the blue, and I started running into her a bit more frequently. After some time, I decided to try to ask her out again. Having learned from the first attempt, I first checked with her that her schedule was open. While she initially could not think of any conflicts, she later said that she would be busy with a group project. Again, this was true.
While it would be nice to know for this situation in specific, I ask in general: what strategies could I use to determine whether one would like to go on a date when an attempt at asking the person out has failed due to a schedule conflict? Should I attempt to reschedule? Should I simply ask? Is there some kind of wording that I could weave into the original attempt that would make an ambiguous situation such as this less likely to result?