Asking to hang out, also not sure if conversations are going downhill...

Backstory: High school seniors, live in different towns about 15 mins away. So I've known this person for about 5 months now, we usually meet at group tennis lessons, it used to be for more than 6 hours a week but now its just about two hours. We only recently started to talk to each other and I've been texting her since the beginning of the month. I'm not going to say I see a lot of "IOI's" because frankly I'm not even sure, but she puts an effort to keep the conversations going even when I send the dumbest of texts, not to mention she seemed to care a lot of how I thought of her when she asked me "what should i look like". We really don't talk during class as we play tennis (kinda obvious) but I really want to hang out with her and get to know her, without asking over text as it seems so informal. Recently though I've been running out of topics to ask, and she takes a while to reply, but i also feel my texts are fucking lame. It used to be rapid fire texting if theres such a thing a week ago now its slow and boring, it's almost laughable.

So, my question is simply that what should I do.. I'm a decently social person, and so is she, if not a bit less social than myself.. its weird.