Great going PTLB!
IMO, the most important thing isn't that you get this one gal to go out with you regular, but that you learn through this about how to handle women, and get relationships going.
3 hours chatting, and kisses on the cheek... how sweet. Yep, she's into you. For the next get together, the best advice I can give is "don't make it seem like a big deal." The next get together should be something casual, each of you don't have a lot invested in it because you're still getting to know each other. You don't want to raise her defenses by some huge romantic date at this time, that would look like rushing things.
Typically, I wouldn't ask a new gal out Saturday for a date Sat eve. But, there's no rules here. If the vibe feels good here, and impulsive is working, go ahead. In my experience, women often don't have a lot planned for Saturday evenings. However, they don't want to admit to that, or seem too easy. There's a risk that she would back out just so she looks like someone who has stuff going on, even if she doesn't. Welcome to the world of chick games.. just treat that as the smoke screen that it is. Tuesday, Wednesday, Thursday are usually best to call about a Sat eve date.
One option is to call Friday or Saturday and say "Hey.. I already have plans for today and tomorrow. However, I'd be up for getting with you Sunday afternoon, or maybe Tuesday eve (or substitute in some other day)." Keep the momentum going with a get together within a week of your last, but don't rush. Options for activities are something low key.. maybe a game of tennis, hike, go to the mall, do a farmer's market, etc... recall your time with her Wednesday, look for things you both would enjoy; don't pick things she'd enjoy and you would hate.
If you still go through with the Saturday evening date, the common ones are drinks, dinner, movies, dancing, things like that. If I were to call for a Sat eve date at this point, and I've called enough time in advance, I'd choose something that's interesting to ME, but not a stretch for her. Your own personal interest in the activity will be contagious, and will sell it to her. Put differently, she doesn't have to worry about being entertaining, or making a lot of conversation; women are more about insecurities than anything else. You can pick from the dinner, drinks, movies, dancing if you want. If there's a party going on where you already know the people, that works well. You can go to some hot spot in town, like north beach in San Francisco, or Rush street in Chicago, if one place seems dead, you can easily bounce, and just stopping at different places can be interesting. Your idea of going out for drinks would work. Going out for drinks somewhere handy to other options like dancing, pool, etc is good too, because you can venture to these other places if you want.
Let us know how it goes... the biggest thing is to remain calm, and being comfortable around women.
