I hate that phrase. 'On the bit'. To get a correct picture of where you want your horse to be, it is better to use the term 'in frame'. In frame can be 'up' into a good elastic contact in a competition frame, long and low with the nose just on or infront of the vertical, or deep and round. People get so fixated about the horse being 'on the bit' that it creates a fixation with where the horses head is, not how the horse is working. It also encourages people to fiddle with the bit, to get the horse 'on the bit'.
The horses engine is his hindquarters. You don't put your foot on the accelerator of your car and keep the handbrake on. You have to get your horse to move forwards
. Your horse needs to want
to move forwards. And you need to allow
your horse to move forwards. You should put your leg on and get a reaction. If a horse is moving forwards, it will find it very difficult to keep its head up. By moving forwards I don't mean chugging along like a Sunday stroll, I mean tracking up and swinging. You don't see racehorses going along like giraffe do you?
Once you have your horse moving forward, and responsive to your leg, you can then start to look to ask for flexion. You want your horse to flex at the poll, softly, and be soft in its jaw. Your hands need to be up, thumbs on top, with a soft elastic elbow - particularly in the walk. In walk and canter your horses head will move a lot move compared to the trot. Your hands need to allow the horse to move forward in the pace freely - so your hands need to follow the horses head. This comes from a soft elbow. Imagine you have a pint of Pimms in each hand, and you don't want to spill it all over you, your horse, or your tack! Your elbows need to be tucked in to your sides as well - no chicken wings!
Start of asking your horse to come soft,
it is easier on a circle to start with. Keeping your outside rein contact constant, gently ask with your inside rein. It is almost like you are asking your horse to flex with your inside rein, but not allowing the neck to bend with the outside rein. As soon as your horse softens, reward by releasing the pressure. Make sure you keep your leg on at all times - remember it is leg to hand.
Keep your leg on once your horse has softened, and walk with your hands (as I said above). In walk try not to nag with your leg (as in nudge every stride or every other stride). Get it so that you put your leg on, and say 'go' and your horse goes. If you feel them starting to slow, then send them forwards again. A horse will very quickly ignore a nagging leg. If your horse drops too low, do not worry, they are just finding their feet so as to speak. If they drop behind the vertical (a common evasion technique) put a bit more leg on to send them up into the contact. At no point do you wiggle the bit, pull alternatively on each rein, or drop your hands down and out.
Sorry for the essay. This is just the basic starting point of getting your horse to learn to come down, gently, without nagging, and teaching them that it's a pleasant place to be.