I, too, would suggest getting a double jointed snaffle. My horse has issues with contact as well. Anytime I pick up contact his head comes up and he hollows his back out. I use the JP by Korsteel Oval Mouth Copper Loose Ring snaffle. He loves that bit.
So what I've been doing is "combing" the reins to get him confident with contact. This should ONLY be done in a DOUBLE jointed snaffle. Basically you slide the reins through your hands, in a hand-over-hand motion, and having a light contact. The more your horse resists, the more drag you put in the reins. When she puts her head down release the reins completely and rub her. Do this first at the halt, then walk, then trot, but NOT at the canter. After she gets the idea, don't release the reins completely when she reaches for the bit, just keep a nice, light, flowing feel on the reins.
Be prepared for this to take quite some time. She needs to become confident with contact, so be patient. Also, I would NOT suggest using a flash noseband. It's just a band aid and covers up the actual problem, in my opinion.