This is an issue I have dealt with numerous times when breaking older horses, such as pasture babies or brood mares. The best luck Ihave had with the "crow hopping" as we refer to it, where they start the bouncing because they don't like whats being asked of them or going on, has caused me problems in the past.
Being able to pick up on the blowing up build up point is a challenge. There are signs given before they start hopping generally. But if a person misses the signs, then what I do is start neck flexion. I will pull the head to my toe and start disengaging the rear quarters, which starts tight circles. I will run a few one direction, then a few more the other direction, as you want lessons in discipline done equally on both sides.
The reason I prefer neck flexion, is that the crow hopping can go into a full on buck and rear if they are going that direction. I am not a fan of holding on while they have that bad of a tantrum. By bringing the head to your toe, they can't and won't go into a full blow up. It also softens them and adjusts the behavior.
I have a 10yr old broodmare that I was breaking for the first time in her life. She did well, but there was resistance as she was very stubborn. Anywho, once we made it past the start, we were working her into lopes under saddle. She had an issue one lesson, and as I stepped her up into a lope, she started crow hopping on me. Unfortunately my head wasnt in the right place at the time, and I didn't catch it until it was too late and she started bucking and kicking out under the lope. I came off and cracked some ribs. It was a reminder session for me to return back to flexion, LOL!
I am sure there are many methods, and this is the one I prefer!
Dixon's Red Hot Ember