Walk somewhere with her. Grab her hand and swing it back and forth as you walk along side of her. Don't let go. If she doesn't let go either, she's giving you permission to hold her hand. : )
If you're worried about her flipping out .. maybe there's a reason for that. Most females won't flip out just because someone tries to hold her hand. She must have other reasons to flip out when you're around.
Horror Movie Date
Place iron rod in her hand and magnet in yours?
If you're walking and helping her up somewhere, reach for her hand and don't let go.
When you're speaking passionately, take her hand.
When you're watching a scary movie and she jumps, you can do it then.
You could pretend to read her palm