yep you're doing everything As you should. the point is, the only time you GO for it quickly is when shes giving you alot of IOI's where you feel you need to strike. Theres a big difference between women that are primed and ready to have sex with you and those who you need to devleop stuff with in natural progression. The prior is one you don't want to miss out on because the opportunity has a slim timeline. Usually the girl is hot and horny, probably right before her period is about to start, or just in general shes been thinking about having some hot sex with a new guy.. or a guy in general. Often times when girls join any type of class, theres a high probability they're joining it to meet a dude.
However, you're doing what you should in your circumstances, and like I mentioned in my original comment, you should proceed to take things slow, develop rapport and see where it goes.
As far as the number thing, I think thats something that you can easily get without having to make it weird.. and is a good initiator without being any blaring signal/sign that you're coming onto her, while also being subtle enough to not signal that you're arent