Consider reading her palm, especially if she's shy. If you're already holding her hand as you walk it's an easy thing to bring it up slowly. Make up good stuff, but nothing over the top. Be ambiguous. If she knows that you're blowing smoke, then it'll be funny and you'll both get a good laugh out of it. If she's into it, grooving on your reading, then that's a great step in. I've had it work for me both ways. In any case, getting to know the palm of a girl's right hand is never a bad way to end a first date.
Haha, this idea seems so quaintly 1970s. Except that in the 70s you didn't have to bother with dating.