<human>: Can you succinctly summarize the text in 1-3 sentences?

I've been on two dates with this girl I met at a church retreat a few weeks ago. She goes to a different school, and I only see her when I take her out. I really like her (we have a lot in common). On both of the dates we talked the entire time. (No difficulty holding a conversation between the two of us).
I initiate conversations over text several times a week on average. The thing is, the conversations aren't all that deep. I was texting her tonight, and she said that the playful, joking side of her isn't who she is most of the time. On our dates, it's been playful, but she's telling me she is a very mature and serious person. She sees herself as a negative person, and she uses the playful texts so she doesn't worry anyone.
The thing is, I haven't been starting "deep" conversations with her because I don't want to scare her off (our "relationship" [which is in no way official] is still only a few weeks old). A week or so ago she mentioned how she was going through some rough times, and I told her about how I was depressed as well (no gritty details, but I told her I was depressed, which is something I don't often admit to).
I don't have trouble talking about myself with people I trust (like my pastor, or my best friend)... but I haven't been as forward with her because I want to have a relationship. And I guess I see spilling my guts and keeping the conversation serious all the time (for this early in courtship) as a bad thing. Basically, I want to know how to initiate "deeper" conversations with her. (holding them won't be an issue, we're both conversationalists).

Most of our communication is via text, and she's leaving for DC (choir thing) tomorrow. Hopefully you guys will help me get a third date when she gets back monday ;)

Any advice on this issue would be much appreciated. More info available on request
<bot>: I want to know how to initiate more meaningful conversations with this girl I like. I want to get to know the real her, and hopefully start a relationship with her.