Maybe she is not paying attention. Are you allowed to talk in your shows? Wake her up before another horse comes around. Let her know through your riding and your voice that you are still up there and you are both still working. And be very firm, yet classy(hard to pull of but worth it) in getting her through her issue. You now know when the problem occurs. Get her mind on you *before* it happens. Are you nervous at all? Pretend you are your favorite trainer in the ring. That works well for confidence. Posted via Mobile Device
My horse will sometimes do that too, took me years & a different riding instructor to make that spook look minimal. It's all about getting your seat deeper, maintaining lateral and shoulder control. It's a long series of various exercises that I cannot explain in a few paragraphs. But a few things that will help you is to get to the show early and ride or longe in the arena beforehand if you can. If your horse does spook during a class don't tense up, sit deeper, relax so the horse can feel your confidence and ride through it. In other words, don't react to his spook and tighten the reins & legs, just calmly ride through it, sometimes spooking is an evasion. Also if your horse is spooking at other horses coming behind him, passing him, take group riding lessons & ride with others in the ring on regular basis. Posted via Mobile Device
If you can, try to practice this are home. Get friends to ride past you going fast, preferably with a horse she doesn't know. This way you can school it outside a show setting and get her more comfortable with it. Even though she doesn't kick, you could try putting a red ribbon in her tail to encourage other riders to give you more space.