My husband a.k.a "the bridling whisperer" can get a bit into any horses mouth. What he does is stand at the horses side with bit in left hand just under the horses mouth. He stands very still so the horse calms down and relaxes his head. Don't move your feet around, just stand there. When the horse is relaxed he puts his thumb into the back of the horses mouth to get him to open and in it goes. He does it in one try every time. My old trainer couldn't even get it in my horses mouth. But he can, by being patient and still. And never let him get away with not getting the bit in. He'll have learned a new trick that tossing the head or lifting it high will stop him from being bridled. Just be patient. Trust me it really works.
Wanted to add that the first time you do this it will feel like an eternity. It took my husband with my horse the first time about 5 minutes of standing still for him to calm. Then after that it became shorter and shorter and now it's done in a few seconds.