What’s the best way to ask out a girl I’ve already known for a year?

I’ve been going to a weekly board game group on the Meetup website and our small group has become good friends over the course of a year.

I want to ask out a friend in the group on a date, but I’m worried that it’ll make things awkward for the Meetup if she says no. We’ve talked a bit during each board game night and she’s seemed genuinely interested in what I have to say. She’s very shy and reserved, but funny and intelligent. But she’s also just as awkward as I am. I’m afraid that she might say yes without actually labeling it as a date. And that she’s just being nice. So I’m not sure whether I should be more upfront or casual about it. Ideally, I’d prefer to just ask “Want to get a cup of coffee this week?”.

Also, she’s rejected one other guy from our Meetup group – he awkwardly asked her out within a few hours of the first Meetup event.

What should I do? Next board game night is this Thursday and I plan on asking her out then.

By the way, there’s an age difference, she’s turning 25 in a few months, and I just turned 31.