the horse puts it's head down on cue, so you have to build in that cue. We cannot and should not force or pull the head down. I don't think you are doing that but just mentioning it.
So, you just have to teach it to respond to some cues. I use the tickling of the reins, openning my hands out to the side (a little like the position for driving a wheelbarrow.)and putting them a bit forward and saying, "Down, Down" in a commanding way but not too abrupt or harsh, more of an encouraging tone, if you know what I mean. And when the horse gives the first bit down and forward, I give a huge release and speak in a sweet , high tone of "Good Boy!".
If she is keeping her head really high be sure that you are not lowering your hands too low trying to pull her down. That can put pressure on the bars of the mouth and create resistance.
Instead, if the horse raises her neck, you just follow her up, so your hands keep that elbow, hand, bit line straight. Your hands follow her up, but you continue asking with a slight "tickling of the rein, more on one side than the other. The horse may try all kinds of things to relieve the pressure you have on the mouth. She might go higher, go left or right or back up, but you only give a release when she either lowers her whole head or at least breaks at the poll and softens a bit. Then huge release and words of praise.
Using the verbal command down helps later when you are trail riding or such to reinforce askig her to lower her head.