How can I (26M) ask out a friend on a date (25F)?

I’m currently in a grad program where I became close friends with a girl a couple months in. Since then, we’ve talked almost every day, either in person or over text. Some days it’s just quick check-ins about school, but other days we have deeper, more personal conversations. We’re also in the same close friend group, and we hang out a lot, dinners, games, going out, etc.

I’ve liked her since early on, but over the past 4–5 months we’ve both been focused on recruiting. My process is done now, but hers is still ongoing. I’m not totally sure where we stand. Some days she’s very flirty and touchy, other days she feels more distant. I think she probably knows I like her, and mutual friends have definitely picked up on it.

At this point, I just want to ask her out so I stop overthinking the “what if.” I’m planning to do it in the next few days and would appreciate some advice.

1. How can I get her alone to ask her out in a natural way? I’d rather not do it in front of others, but we usually see each other in group settings. I also don’t want to invite her to my place or hers in case she isn’t interested.
2. How direct can I be? Frame it as dinner or an activity? For example, something like “Would you want to you go out for dinner with me, just the two of us?” I’m leaning away from using the word “date” to keep it lower pressure.
3. If she says no, how do I keep the friendship strong and avoid things becoming awkward? She genuinely means a lot to me and I don’t want to lose that.