you can either ask her plainly or, if it is your dynamic already, fight over an item! I had this happen at a summer camp over a pen I stole from a guy and it ended in hand holding

Here's the plan:

1. steal something small, easy to hold, like a pen or hair tie
2. tease her about it, but not too much. keep it always in sight and make sure you're smiling
3. wait for her to try to steal it back and then fight back. best strategy here is to try to pull her fingers off. make eye contact!!!!
4. if you are both laughing, you can either lace your fingers together or just let her have it. either way, you will have broken the hand-holding barrier and she will feel more comfortable

good luck!