You can get a decent curb bit for not that much money. I don't ride in one, but my friend does. The junior cowhorse bit might be a good enough choice. YOu would get more brakes.
I think many if not most horse would spook and maybe bolt if cows come running upt to them. Mac would be GONE! But for me, I want to have lateral control, so it he did start to bolt, my plan would be to pullon him around with one rein and ask him to face the thing that he is trying to flee. If he got to a gallop, I would not try to one rein stop him when he was at that speed, just as you said, too likely to cause a fall.
If you do ride G in a curb , watch and observe to see if this cause her to become overly reactive to the rein/bit and get back into throwing her head in the air or running around very stiff and hollowed out and giraffing.
Using a curb means you have to be that much more careful with the timing and use of the bit. But they are not devilspawn. Might be a good thing. Who knows.