Are you riding English or Western? I'm going to assume English because that's what most lessons are. Maybe I'm wrong about this but ask your trainer if you can ride western until you get better riding skills and more confidence. If not, I would sit like you are riding western. By that I mean to sit back on your tailbone. Instead of riding straight up and down, lean back a little and let your lower back curve or roll. IMO this would help you to learn to balance and be able to stay on the horse better.
As a beginner/novice rider, you lack experience. Lack of experience leads to lack of confidence which leads to you being nervous. A horse can sense how the rider feels. If you're nervous, the horse will get nervous which is why the horse spooks and bolts on you. I think by having you sit straight and having you keep your legs on, it makes your body more tense than from just being nervous. When riding in an arena, have that horse walk around but keep walking. Don't control where he goes, just let him walk. As he's walking, rub him all over as far as you can reach. This will help you loosen up and be more relaxed.
As for the bucking and trying to shake you off, it goes back to you being nervous. A horse is looking for a leader as a rider. They want someone that is confident and in control. If you're nervous, that makes them nervous and uncomfortable. When the horse does anything to get you off, have them do circles but change directions often, or have them do figure 8's. Get them working and having to think about what they are doing and not thinking about how to get you off.
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