If you want to stop bouncing while riding a horse, there are a few essential tips to keep in mind. Firstly, ensure that you have a correct and balanced seat, distributing your weight evenly. Relax your hips and follow the movement of the horse with your body. Engaging your abdominal muscles will also help stabilize your position. Additionally, practicing specific exercises off the horse can greatly improve your balance and core strength, ultimately leading to a more comfortable and stable ride.