That is a good bit to use, imo.
What I would be doing is doing exercises that will get her bending and flexing for you laterally. Start on the ground, either with the bit, or a rope halter (less to lean on), and take up the lead rope, or one rein, and bring it up toward the wither (or saddle horn if she's saddled)...take up enough slack so that she has to bring her head back a bit, and wait for her to "give" to the pressure. She may go in circles for a while, but just stay with her, and wait for her to come back a bit and release the pressure on the lead herself, then let the lead rope slack, pat her, and try again. Gradually she will be able to bring her nose back further and further, and will give to the pressure quicker and quicker; do that on both sides.
When you are in the saddle, do the same stuff, only you will bring the rein to your hip and rest it there til she gives; again start with taking out only a bit of slack out, and go from there; eventually she will be able to bring her nose right to your toe without any trouble, and will do it readily. What all of that is going to do is give you the advantage laterally, over all of her movement. When she starts to speed up, or decides to try and go her own way, all you should have to do is pick up one rein and get her to 'change her mind' quite quickly...This lateral flexion will also give you the basis for getting her to collect and be flexible vertically, because she will be soft to the bit in either direction, it will be easier for her to understand when you ask for it vertically.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."