How do I get my horse to let adults ride him?

I have an older horse. He is about 15. He is half Thoroughbred and half hackney, so he is the size of a small horse/large pony. I have talked to a horse trainer, and he said he should be no problem to ride after a bit of work. Someone used to ride him, and he would throw her occasionally. He will let a child ride him, but he throws adults. I can saddle, groom, clean out feet, halter etc. I can bridle him, but he hates the bit. So does anyone have any ideas, without hiring a trainer? I have been reading John Lyons books, and it states a novice can train, it just takes longer. Thanks in advance.