Get your basics totally downpat before you worry about where his head is. If he thinks that a bit of contact means stop, you havent got a good enough go button. Does he move off your leg immediately from slight pressure? Or does it take a bit to get him moving? Will he yield from your leg, will he maintain YOUR pace until you ask it to be changed? Are his paces forward, marching and active, off the forehand...? Or does he just run fast making you think that he's 'forward'. This is what people with ottb's say, "Oh, my horse is very forward", no running on is not forward, I bet if you asked for the horse to move off when they want to stay slow, they won't do it.
How are you asking him to come 'onto the bit'? Because if you're just pulling back and putting leg on that is just giving him conflicting aids and won't do you any good. He should be responsive, but not hyper sensitive, to the leg and willing to keep moving each time you touch him with the leg. Getting a horse to take a contact that doesn't understand the concept is not something you can teach over night. It takes patience, and good, solid basic work as desicribed above. He should also have a basic understanding of responding to your back/seat.Work him onto a circle, and legyield him in and out. Lots of rein changes, transitions, leg yield and shoulder fore if you know how to teach it. Always keeping the rein contact steady, don't pull, but don't give your reins away. Just leave the contact there for him to have a feel of, and by making him engage his hindquarters via transitions (trot-canter-trot are the BEST!), changes of rein and leg yield/shoulder fore, he will start to work and loosen his back, which in turn will encourage him to pick up a contact on the bit.