Answer

By Your Horse

Natural Horsemanship Expert Charles Wilson says:

The clue to this problem lies in your phrase ‘I find I tense up’. Your horse will feel this tension, and his instinct will take over, resulting in the flight behaviour you have seen.
Make sure you get to the show in plenty of time. Walk him in-hand around the grounds, letting him eat a little grass – have time when you can both relax. Lead him to the outside of the collecting ring so you can see how he is in close proximity to the other horses. If he is nervous, keep him there until he becomes desensitised to the whole situation. This may take a long time and you may even have to return home without competing. But he must be given the chance to get used to the sights and sounds in his own time, without the added stress of you being on board, and having to compete.
Once you feel he is coping with being near the ring with you on the ground, you can get on board. If he becomes tense, walk him quietly around the show field for as long as it takes. Once he is relaxed and listening, you can trot a little, and then canter when you feel he is rational and calm. Do not hurry him. Only then will you proceed to the collecting ring. Wait outside until he is calm and then walk quietly around the ring. Expect this to take time, and reward any improvement in behaviour. Do not punish him if he loses it.
We all get nervous, but successful riders learn to control their feelings. This will be key to improving your horse’s reactions. Your arms need to be relaxed, to stop tension being felt down the reins. Do not hold the reins tight, and make sure his bit is mild.
A simple snaffle bridle and cavesson noseband should be all you need.