"Drink" was just an expression. Dinner is equally good. Yeah, find a way to get her alone, even for a minute, and, maybe, since the time is so short, be assertive and forward. Put your arm on her shoulder or touch her hand warmly, while saying, "someday we're gonna have to go for dinner together, I know this great place and thought that of all people you'd appreciate it a lot". Of course, try to find out what she likes to eat and don't take her to an indian restaurant if she hates it. I think that being warm, straightforward, make a quick move, can work.
Just to give you an example, I met this girl yesterday, 25 years younger than me, at a small restaurant, she was behind me while ordering at the counter, and I said out loud, I wonder if this is good, "it's great", she said, "had that before". So I immediately I ordered it because I knew I had an excuse to talk to her. She sat at a nearby table and said "yeah, it's great, thanks", and so on. "Where are you from?" "Atlanta", she said. "And what are you doing here?" I found out all about her and engaged in a conversation. I then said I had to go, got off my table, but stopped at her table to say a "last" word. The "Last" word lasted 5 minutes, so she said, "why don't you sit down". And I did and continued talking and talking. The trick is never to let her think you're boring... At some point I touched her hand on purpose, and said, "oops, sorry, I've even touched your hand, ha ha, that's how interesting our discussion has been". Again, to make a long story short, I ended up getting her phone number and email. I've already texted her and will try to meet her again.
Women like sex a lot, more than men sometimes, but will go long ways to prove that they're not interested. The sure way not to fuck is to talk about fucking from the start (with rare exceptions: women who have realized that the game is silly, but those are very very few). The best way is to talk to them about everything except sex.