In simple terms, put some a few pounds of pressure on her mouth and calmly say the word, "Baaaaack, baaaaack...". Not enough pressure to cause a head throwing rage, but enough that it annoys her. Use a snaffle bit for this phase. Eventually, finding no other way to alleviate the discomfort, she will take a step back. If she tosses her head, goes forward, sideways, or anything else, keep that same pressure -- no more, no less. You want this to be a clear aid to back and nothing else will do. Sit quietly on her back, well balanced and not leaning forward. Once you feel a leg take a step backwards, throw down you reins. BIG RELEASE and praise!
Keep on doing this until she will step back once readily when you ask. Eventually ask for two steps. Every step she takes, release pressure for a moment as a reward and continue asking her to back with soft vibrations of the reins.