Although I can't quite tell what started the bolt on this video, it's quite common for beginner riders to go off balance and tip forward after even a small jump. In fact, it's an inevitable part of learning, but more serious problems then arise because a horse understands leaning forward as a request for more speed. English riding instructor Heather Moffett, cleverly and appropriately, calls this curled position the "fatal crouch." The situation typically becomes even worse when the rider tries to slow down the horse by pulling. Again, it's a natural response. People instinctively want to bend forward to protect their soft bellies and to use their hands to force a stop. Unfortunately, this clashes with the horses' instincts to go faster when humans tip forward and to flee in terror when people grab and pull at their mouths. So, if a rider wants a recipe for a bolt here it is: Lean forward and pull.
Anyone wanting to see how experienced riders slow a horse down has only to watch a televised horse race. After the finish line, how do jockeys slow and stop their horses? Do they crouch and hang on tight? Hardly. That's what they did to get their mounts to try to break the sound barrier. To slow and stop, they stand straight up and slowly lengthen the reins.
Going back to the video, it also shows how pulling can also cause a horse to rear. This far more dangerous situation is from seconds 30 through 38 on the video. The horse had stopped, but the rider's adrenalized tension and lack of experience likely caused her to pull when the horse fidgeted. Luckily, this rider respected her instructor enough to follow her instruction to "stop pulling." Almost anyone who's ever taken a riding lesson understands how much bravery and discipline it takes to surrender to instruction and respond appropriately when the body is screaming clutch the reins and hang on for dear life.
Learning to disregard instincts is among the most difficult challenges for a rider. This is one reason my students typically spend months and months on the longe. And even when they go off the longe line, they ride in bosal hackamores or natural horsemanship halters for a long time before their introduction to the snaffle. A beginner can do enough damage with even a halter, but my no-bits-for-beginners policy helps keep my horses sane and,in turn, keeps my students safer. Meanwhile, they learn that even riding with a halter means working on lightness.
It takes a couple of years to develop a good seat, but it's generally a lot longer before a rider grasps--pun intended--the limited role of hands in good riding.