Greetings from Denmark!
I've followed this thread for a long time, and it has given me a lot of valuable tips on text gaming, but now I have a problem of my own that requires help - so here goes:
I met this girl at a local bar about a week ago. She's kinda in my social circle, meaning that we've got quite a lot of friends in common, but we did not know each other personally. Last friday she came up to me while I was talking to one of our mutual friends, and we got into conversation and had a lot of fun. We ended up dancing, but at the end of the night she disappeared and I went home.
She had told me to find her on facebook, and so I did. I got her phone number without problems and started texting her. In the beginning everything was going well. I used a lot of call-back humor from the night we met, while also getting to know her better.
But suddenly the conversation died out, even though I tried to bring in new and interesting topics. She didn't answer me, so I decided to wait a day and text again. She answered, but very shortly, and she did not seem very interested. So I decided to stop texting her and deleted her number.
This saturday evening she suddenly texted me, asking me if I planned to go out. I played it a little formal and told her maybe, and she seemed very excited to see me again. I ended up going out with a couple of friends, and she came to the bar where I was to see me. Unfortunately, she had to leave almost immediately, so I couldn't close her, but we did text back and forth while she was on her way home.
Yesterday I texted her again, and conversation was fine. She invested as much as me, but it didn't seem to escalate, and the conversation was a bit static. This is where I need help. She seems kind of reserved, and I'm not really getting that closer to her, and I was hoping to get some help on how to move conversation to the next level and set up a day two. So here's a sample of last nights texting, translated from danish:
ME: Did you get home safe last night?

HER: Yes, I did

How about you?
ME: Yes, but very late! So I'm looking forward to going home and relax tonight.

HER: You haven't been home yet?
ME: Yeah, but I had to get up early to look at an apartment. So now I've got a date with my duvet.
HER: Was the apartment nice? I've longed for my bed as well!
...
ME: I feel like watching a good movie. Can you recommend one?

HER: I can recommend handball on TV2 (danish TV-channel)

But The Butterfly Effect is a pretty good movie.
ME: I had forgotten! Are you into handball?

HER: It's exciting

I've played myself.
ME: I think so too

Why don't you play anymore?
HER: Haven't got the time

And I like running better.
ME: Were you any good?

I run a bit as well - I should do it more often.
HER: Hm, after 7 years of practice I should be able to play okay.
HER: Yeah, I should run more often too

ME: I hope so

I suck at handball, so I stick to soccer. Are you training for anything special?

HER: Soccer is great too

I'm planning to run the Copenhagen Marathon. My training programme begins tomorrow, so I've got 20 weeks.

ME: Cool! How did you get that idea?
HER: Because I've done it before

ME: Awesome! Then you can - almost - outrun me

HER: I'm not at my best now, but I will be

ME: If you need me to drive behind you and cheer for you while training, just say the word

HER: Haha, like that would help, but thanks

ME: I'm pretty good at it! How fast did you ran your last marathon?

HER: It wasn't a marathon, but 58,5 km on 6 hours - and a half-marathon on 2 hours.

ME: That's quite good. I suppose you have a goal for this years marathon.

HER: Yeah, or maybe

Depends on how my training goes. But I'm off to bed - goodnight.

ME: Goodnight. Sweet dreams.
I hope the sample isn't too long. As you can see, I have no problem making conversation through text, but I'm having trouble taking it to the next level and get her to commit to a day two. I hope you can give me some advice on what to do next, and what I could have done different.
Thanks in advance.

To be honest with you, this seems like a conversation a 'Nice Guy' will have with a girl. It's a nice conversation. Don't get me wrong. But, it's too flat, too dull, there's no flirting, there's no double meanings, nothing.
That is NOT the kinda conversation you want to have with a girl you're interested in. It would put you in the "Safe" category and that's a bad place to be.
So, I'd suggest you to start flirting here, outright flirting, teasing sexually if needed, just to get the mood to a place where some tangible progress can be expected.
Also, during these physical meet-ups with the girl, try to kino-escalate on her. You too. DiCarlo Escalation Ladder. Go. Get that.
As long as you're taking chances, you'll get chances to get somewhere.
Play it safe and you'll get nowhere.