Sounds like she's not respecful to the bit at all. How well does she stop in the Argentine?
First, you've got to get her listening to seat and leg cues, not relying on rein. When you want her to stop, first ease up your body language, then sit down and put your legs slightly forward, then say 'whoa,' and only then, if the hrose has not yet stopped, pull back with increasing pressure on the reins until the horse comes to a complete halt and relaxes a smidge. Then, exactly then, and only then
, release the rein pressure. There's a definite progression and order in the cue, yet the sequence in its entirety takes less than a second. Repeat until your horse is stopping as you sit down and say whoa, with no need for the reins to be pulled.
As you're transitioning into the snaffle, too, I'd recommend double-reining your Argentine like a Pelham, so you can use it in the most effective way: