Looking to expand friendship into possible relationship

I am a twenty-something interested in a twenty-something, but I don't know how to proceed from there. We knew each other in college, and we recently got re-acquainted over the past summer. She met my friends, we roamed around DC a bit, and so on. Now I'm wondering if we can be more than friends. I'm not even asking for an instant relationship, I'm just hoping for a mutual understanding that we'll see how things go (fingers crossed for hand-holding privileges). The thing is, though, I can't tell how interested in me she is. She's often quiet, a lot like me, and it can be really hard to tell if she's enjoying herself. On the other hand, she trusted me enough to call me about picking her up from the metro after missing her bus at night, and we may be planning to see old friends at college together (well, maybe not together, since they're her friends, but she trusts me to drive). I guess I'm wondering is 1) Is what I'm looking to ask her a good idea and 2) What is the best way to go about it?