How to handle this rejection and maintain friendship

I have a friend I find really cute—we work together, see each other every day, and get along famously. We’ve hung out quite a bit, and I wanted to test the waters to see if we could move from being just friends to maybe dating. So, when planning our next hangout, I made a point of using the word date. She didn’t give me a clear yes or no.

A minute later, I had to turn back because I’d forgotten something, and that’s when I unexpectedly found her crying. She asked for space. Exit stage. Soon after, she texted me, saying she wasn’t interested and didn’t want to hang out outside of work anymore. Now, she’s avoiding me at work, so I’ve been giving her space.

So my first question is:

Why would asking someone out lead to a reaction like crying?

2. Most importantly, how do I approach this without making it awkward? I’m not heartbroken over being rejected, but I would be devastated to lose my best friend. I truly believe I can continue being her friend without wanting or expecting anything more, but I don’t know what to say to help things feel normal again. I’m also unsure how to encourage her to talk to me, or how much time and space I should give her.

3. My old man would probably tell me to “be persistent” or something along those lines. And while I do want to date this girl, I don’t want to risk damaging our friendship in the process. With college and everything else, we’ll be separated in just a few months anyway. Part of me wonders if maybe she does like me, but is hesitant to start something knowing I’ll be leaving. The truth is, I would stay if she were my reason to. The question is—how can I bring this up (in the spirit of persistence) without making her feel like friendship isn’t an option? I dont want to disrespect her bounderies or lose her trust