Why does a horse run with it's head in the air?
THis seems to be the question you might ask yourself. It might be habit, it might be in some ways associated with the breed or build of the horse, or it MIGHT be painful saddle fit. So, that is one thing you want to be sure of before you go even one step farther.
The bit is another thing that might be causeing pain, thus an avoidance behavior. Not necessarily the bit, but the mouth if it's got any rough teeth or other issues.
Once that is clarified, then you can look at the giraffing as a pure behavior issus.
You got a lot of good advice and stuff about collection. Collection is all good and well but it comes farther down the line from what I percieve you are faced with right now. It is said that collection work from rear to front and this is true, but you cannot collect a horse if "the front door won't close".
So, I think you need to have the horse bring its' nose down a little first and foremost. For one thing , as you said, you don't have very good control when the horse is going above the bit like that.
One good thing, however, it's easier to train a horse that comes above the bit to come to the bit, than it is to train a horse that comes behind the bit to come to the bit.
I am of the camp that when she puts her head up, you lift one or both reins (but one with more contact than the other) and put on a steady resistance to her pull, ONE OUNCE more than she does. She will move around trying to find the way out of this resistance and when by chance she finds that dropping her nose (and be sharp to look for the tiniest drop that she might make) you reward her with a good release. You will have to do this many times. If she gets stuck and won't make a choice when faced with this pressure you put on her (or rather she puts on herself, because remember, it was she that put her head up in the first place) , if she gets stuck, help her by putting a little leg on which will get her to move forward and thus put her nose down,
Work on this and only this for awhile. Practice it all the time. It is like Kevin said, you must develop real feel. Once you have this, it will be much easier to work the horse from back ro front because you will HAVE a front to work toward!