when bending a horse, it is good for you to bend yourself, on ground, first of all just to pause and think about your own body mechanics, and i would like to urge this technique for all schooling exercises you do, and when it comes to thinking of you on the horse, imagine a small child on your shoulders, thinking about how their weight distribution can balance/unbalance you.
so you are sitting on your horse, and your horse is basically as seen on a merry-go-round - it has a pole travelling through it body which is its pivot. in this situation, you are the pivot - you are the child on your shoulders when you are on ground. so it is important to remember that when you move your weight to the outside, your horse will travel to the outside to catch your weight, and balance itself up.
imagine we are on the right rein, and we are passing the long side into a corner. halfway between the middle and corner marker, you will have started to look round the corner with your gaze, and as you ride into the corner, move your shoulders to the direction you want to go. your hands stay still, quiet and even, not dropping or rising, as this removes the quietly established equilibrium between your hand and the horses mouth, it just comes from your shoulders. to think about your hands being very quiet and still, may i suggest holding the reins with literally just your thumb and index finger, the other two resting on the rein ready to give a gentle squeeze if you feel the horse diverting his attention to something else, the pinky in its normal position.
guide your shoulders around that bend with your belly button - i think to think of mine as the keen forward driver, always anxious to move in a straight or bend wherever we go, and always regulates my position is rising trot. make sure you just turn your shoulders, and not your seat bone as this could send you flying! your inside (right leg on the right rein) remains at the girth, acting as the invisible boundary that keeps yoru horse on the track even though you have shifted your shoulders, and the outside leg comes back behind the girth. this actually has the power to free up the outside leg (on the right rein, left) and allows it to extend round that corner.
if you walk round on a circle yourself, on the same rein, you will find that the right leg is your pivot leg, and you put your weight into that leg to guide you round the circle. i know i was just talking about bending round a corner here, but for riding a circle, it is always a good thing to remember that the inside leg is the pivot leg of the horse.