<human>: Can you condense the text into three sentences or less?

Alright, I should be able to keep this pretty short.

I met this girl online, she's awesome. She's very mature for her age, and has huge ambitions in life. She's sweet, beautiful, smart, and she's not the typical party girl who is shallow or uptight.

I feel like she's trying to play the chase game. I HATE the chase game. I don't want to worry about the social stigma that is behind it all. If I'm into someone, I want them to know, and if they are into me, I want to know the feelings are reciprocated. 

We've been on 2 dates now, both of them went amazing. Took her out for a very nice dinner and drinks for the first date, 2nd date was more casual and we went to a movie (it was a horror movie and she was clinging onto me for the whole thing). After the first date I decided to go about things a little slower to build a relationship, since this isn't a girl I just wanted to sleep with and have it be over. Kissed her on the 2nd date, and told her I hoped to see her again soon, to which she replied "You will :)". I KNOW she is into me, but then when it comes to texting she seems cold when I'm into it, and hot when I stop replying quickly (I don't overload her, I just text her maybe a few times a day, sometimes more depending on conversation, sometimes not at all). And when it comes to asking about going out, she is generally busy, and when I say, "Alright, no worries", then she starts offering days that work for her, after I've already tried to get that info out of her.

Now, I want things to progress, but how do I tell her that I want to get past these games. Do I just ask her if she's interested in a relationship ASAP? Or would that just put her off making me seem desperate.
<bot>: I don't want to play these dating games of chase, but I feel like it's my only option. It's rough when it's a girl who I'm into and she seems into me.