Neither will you learn by a war of attrition – trotting endlessly without stirrups as “it’s the only way to get a good seat”. The horse must be carrying himself correctly for you to be able to sit and you must be carrying yourself correctly for him to be able to do this in the first place.
When the horse offers his back, sit – but only for as long as it feels good for both of you. Either of you may break the cycle; he by starting to drop his back (go hollow) or you by losing the rhythm of the stride in your seat /hips. As soon as you feel any deterioration on either part – go rising until the horse gives you his back again. In the beginning you may only sit 3 good strides at a time before you need to rise. Working like this you increase your own and your horse’s strength, without stiffening or tension taking over, and pretty soon you’ll be sitting 6, 10, 20 strides!
Learning the sitting trot is one of the hardest things because you have to discover for yourself the precise muscular effort that is involved. It isn't a simple case of relaxing because if you did that you'd just bump to the back of the saddle!
Most people try to think of sitting down into the horse. To be able to sit the trot properly you have to let the horse come up under each individual seat bone and move the hip up and forward. The other feels as if it goes down / back. It is this mis-timing of this individual up / down phase leads to bumping and jarring. When the horse reaches the top of his up phase you have to consciously think going back down with the saddle. Waiting for gravity will be too late! As I say you have to allow this to happen, but at the same time you have to match the forward motion of the horse from within yourself.
You have to exert this forward motion with each stride in a two-time rhythm. The trouble starts when you forget to go down with the saddle with alternate seat bones. Trying “to sit still” will end with the inevitable slap up the backside! You need flexible muscles around your hips and lumbar back - the most notorious for being the complete opposite. You need to be able to contract and relax these muscles at will. In addition you must support your torso with your midsection muscles so that you are sitting balanced over your seat bones with your hips (joints) under your shoulders. Only from this classical alignment, with your vertebrae in neutral spine can your body absorb the motion correctly through the hips and spine.
Those riders who nod their heads with every stride are usually guilty of sitting on the back of their seat, with raised knees and locked hip joints. The “shock” is not absorbed and comes out at the extremities in the form of the unsightly nod and/or wobbling hands and belly dancing tummies.
Think of your torso making a capital "D" not the awful reverse "C" that is the norm. Your back is the back of the D (don't stiffen though) and your front line pushes softly forwards to make the round front. The "C" shape you so often see is the result of riders trying to absorb the movement with a collapse inwards - ugly and ineffective.
If you are someone who “bumps” in sitting trot and canter, you may, inadvertently have been using your hands to keep yourself “with” the horse. This is one of those phrases to throw away. To me this implies that the horse is in charge and you follow him. Think much more of leading the horse from your centre - – not that you want to get a head of him – you want to synchronise your movement so that you are together.
The same principles apply in canter. Give your hip joints to the horse; let him move them. These is absolutely no need to push, shove, grind or drive in any way. The movement of the horse will do all the necessary opening and closing of the joints and move your pelvis. If you try to “sit still” you will block his hind legs from coming through. Your upper body stays softly upright ( no rowing motion of the shoulders ) maintaining the capital 'D' effect.
It may help you to think of sitting up tall-taller-tallest, as the movement of the canter stride pushes your seat forward. This will involve engaging those midsection /pelvic /lumbar muscles again, within the rhythm of the stride, to stabilise your torso whilst allowing your pelvis and hips to synchronise to the horse.
A superb analogy for canter and sitting trot is to think of what happens when you bounce a ball against the ground with your hand. As it comes up from the ground you raise your hand with it until it reaches the top of its rise and only then do you begin to push it back down again. Meeting it as it's still coming up causes a "bump".