Should i ask her out? Advice for a newbie at dating?

So theres this girl at my uni that i like. I dont know her too well and shes not in my classes, but shes in the same study group as me. The thing is, said study group only meets very occasionally but i really want to get to know her better. She definitely likes girls no question about that. I think i even caught her checking me out a few times. Even so, im still not sure how she feels towards me. It looks like its probably a mutual attraction based on various things that occurred.. but im not entirely sure. And i dont exactly want to spend anymore time racking my brain trying to figure it out. That was me my whole life after all. Just sitting there trying to figure out if my crushes liked me but ultimately doing nothing and waiting for something to happen. Perhaps ive suffered one disappointment too many, or perhaps im just more comfortable with my sexuality now. Whatever the reason may be id like to avoid doing that again like the black plague. Its just that ive never done anything like this before and im kinda lost.

Over the last couple of days or so we have gotten a bit more familiar so i was thinking maybe i should ask her to have lunch with me? Does that sound like a good idea? I was thinking of asking over message since its kind of rare to run into her, Or maybe just wait to run into her in the hallway to ask in person.
Any advice for a newbie like me whose never asked anyone out before and is kind of like.. really nervous about this?