Yep I stand corrected about her shoulder, now that you've put the confo shot up it looks like it has a good slope to it.
The reason she's less bouncy when you slow her right down so she's not tracking up, is that she's dragging her feet along and so there is barely any motion in her back and no 'bounce' in the gait. You can sit trot any horse is you pull them back to almost a walk ;)
I would say when you ride her, even if she's not on the forehand (I haven't seen any photos sorry!) she's probably got a very stiff and possible hollow back thus is working entirely from her legs rather than using her whole body. You can equate that to sitting on an ironing board down a rocky slope if your horse is naturally bouncy! Some horses of course, are just not bouncy, often they're the ones will less movement in the joints, so horses that have fairly 'straight' legs in their gaits will be easier to sit on as there is not so much movement being carried into their back by the gait. I bet most people would sit to struggle a dressage horse that is entirely collected and in piaffe. It may look lovely and easy to sit on, but the bounce in the movement is very strong and can throw you out of the saddle if you're not able to sit trot effectively.
Just to sum it up, I would certainly say her bouncyness if from her just being a 'bouncy' horse. As smrobs said, she's short and steep in the pasterns, and arab breeding so she's probably just going to be a bouncy horse. When a horse is so naturally bouncy in trot, you can never make her smooth, instead you have to learn how to sit trot her and absorb the impact. It will help for her to be able to learn to swing her back and carry you rather than travel all legs, but that would require a reasonable dressage coach and you to have a basic understanding of how engagement works. Which is another thread altogether!