Getting a horse on the bit is pretty difficult if neither you or the horse has ever done it before. I think it also requires a certain level of fitness and suppleness. My horse was too stiff and out of shape when I first started, and we did not even try. We got her moving off my leg and seat better and leg yielding and bending well first. I have been taking dressage lessons since June, but did not try to actually get my horse on the bit until 3 weeks ago. I could not do it. My trainer got on and explained to my horse what was being asked, and she managed to get it for a short period. We are now able to go around on the bit at the walk for just a few times around the arena before her neck muscles need a break. She is a little rounder at the trot, but is only actually on the bit for a few strides at a time. Also, I was told that it was ok for her to be heavy in the contact at first, that she would get lighter as she got more fit and understood what we wanted better. I know my mare hates having her mouth pulled on, and she is ok with this as long as I don't ask for more than she's ready for and remember to give some release on the inside rein.
This might be one where asking for help from a more experienced person would be warranted. I could never have taught my horse to do it by myself, because I never would have tightened my outside rein enough, and I really didn't know what it felt like to have a horse truly on the bit, so I'm not sure I would have rewarded the right thing.
Tug on anything at all and you'll find it connected to everything else in the universe.~John Muir