See? Now we get a little feed for discussion :P
In ''my'' world, ''on the bit'' means that the horse is responsive to the cues, not necessaily that he leans onto the bit/hand. Since I ride with a western curb (and beside that generally dislike too much contact) I wouldn't want him to put preassure in my hands. The leverage would make it too much. However, if my hand gave him all of the rein and my seat allowed it, he would stretch forward and down. Like here; still little to no contact on this urb (hackamore) but here my seat and weight ask him for a regular trot with longer strides and less collection.
He does however have a high headcarriage and we have had some issues with getting a really low headset in other gaits than walk. (perhaps because I'm reluctant to give his as much rein as he wants to keep a low headset in a faster gait, since I'm a little chickenish that he'll run and I won't get the rein back in time.. it's silly really since he stops on voice and seat, but.. I'm a control freak) it is much better since I switched to a curb though, believe it or not. He relax better in that and will seek forward much easier without curling up or tucking the nose in. He stops on voice and I sometimes ride in either a halter or completely bridle-less, so it's not that I need the leverage.. but he's more relaxed with it.
I do definetly ask/cue him to slow down his forward movement and direct it more up, but I don't do it with my hands as much as my seat. I sit back, ake a deep breathe and pretend I'm already riding the move, gripping some with my thighs and gently squeesing with my lower legs. My hands only stop him if he tries to run out of the cue instead of listening to it.
As I mentioned, the really low frame is difficult, but we're getting there and working on it. If I'm not asking him to ''work'', he'll be a star gazer with a deer neck and hollow back, or stick his nose and neck straight out. That I use my seat rather than my hands to get his nose down isn't really an issue with collection from my point of view.
An example of ''natural'' to him, vs when I get myself together. Also two gait-pictures, and these are not really collected as such, he's running the fastest he could withut starting to pace, at that point. The rein preassure is about the same, the differense is that in the first picture my body was stiff and braced and in the second I ''held'' him between my legs and directed my own energy. But I think they show the differense between ''sitting on'' and ''rding'' him :)
Not that any of these pictures show anyting about how collected he is in the first one. Quite the opposite, the background story could influence with how you judge the picture, and this was all about judging that picture.
But if he's not ''on the bit'', at least he's ''on the cues'' ;) He's not a well schooled PRE that will just collect himself naturally just from getting a little energized.