So, to begin, here's what went down:

I'm sitting in a (quiet study) library at my university when a cute girl walks in and sits down across from me. I sit for a while doing my work but can't stop noticing her, while she does not seem to look at me once the whole time. However, I didn't want to let that stop me, so I told myself I am not leaving until I ask her out, or at least say something to her. I have to pee so I ask her if she can watch my stuff while I go to the bathroom, she nods without saying anything, and I leave.

Then, something unexpected happens. I'm in the bathroom quickly going over a direct way I can ask her out for coffee, when the fire alarm goes off in the building. I quickly rush back to the study area, hoping not to miss her. To my surprise, she's sitting there, not moving, while everyone around is scrambling around to pack their stuff. I take this opportunity to ask her if she plans on leaving, to which she shrugs and says "I don't know." I hoped to use this as a chance to talk to her but now with everyone else leaving and security coming through telling people to evacuate the building, I thought it would be suspicious if I were to just sit and wait for her, so I start packing my stuff slowly, hoping she'll do the same. She doesn't. I decide since I'm packed up that I'll go outside, wait for her to come out and then talk to her some more. I go outside and 5-10 min later see her walk out and briskly leave in the opposite direction. I missed my chance and feel like I fucked up by not asking sooner, but then again what are the chances of a fire alarm happening then and there?

Anyways, this left me with 2 questions:

1) What would have been an ideal way I could have responded and made the most of the fire alarm situation to possibly talk to her some more? It's probably clear I'm no expert at this.

2) If I am sitting in a silent library and face the scenario where I am trying to ask out a cute girl sitting across from me, what is an ideal way to talk to her and ask her out without irritating her because of the distraction from her studies? My original "script" was to just be quick and direct and say something like this:

"Hey, so I know I'm a stranger and all but I think you're kinda cute and was wondering if you'd like to grab coffee sometime. Here's my number, just shoot me a text if you're down. I'm [name] by the way."

However some of my girl-friends have told me to at least have a conversation so it doesn't come off as too sudden/creepy. I'm still lost on thinking of a good way to start a conversation in a quiet library, where people go to avoid distractions.

Thanks if you've read this far, and any help here would be appreciated.