Doing the sitting trot with no stirrups, while it is good practice to develop an independent seat, is not really going to help you a whole ton. You need to learn to use the stirrups to create a "bow" shape with your legs around the horse and really use the shape as a shock absorber. It's tough to explain but your feet are going to swing in and out at the same time your knees swing out and in, so in the moment of suspension in the trot your legs will be almost straight and at the "down" moment, your legs are going to be bowed around the horse like brackets ().
In order to make this happen, first of all your stirrups have to be the correct length, after doing 5 - 10 minutes of no stirrup work, stop, don't move your legs and adjust the stirrups so that they are hitting your ankles, this should be correct. If they are too long in a few minutes, then shorten them.
Then you need to have a really free pelvis and be able to use your back and ab muscles to hold yourself in the motion. Sitting with your upper body extremely slightly behind the vertical can be useful to get the motion, but don't make a habit of it. Your back should be relatively flat and your ab muscles should hurt. Keep your elbows tucked into your sides and drive your shoulders towards your hips until your elbows are in contact with your hip bones.