I have a horse that much prefers hackamores to bits but he goes very well in a double jointed happy mouth and a Mullen mouth
Some horses prefer single jointed bits and some prefer double jointed. If you were using a single jointed snaffle, try a double jointed snaffle with a bean or lozenge in the center. If you were using a double jointed, try a single jointed. Also, do not use a loose-ring bit unless you have very quiet hands. Try an egg-butt.