There are many different ways you can train a horse to take a bit correctly, and your horse probably knows how to do it already, but if you are asking differently than he was taught or are fumbling or unsure, then he is probably taking advantage of you even in the bitting process.
It's too difficult to describe how to do it correctly on "paper," so that you can picture it, and a lot depends on the moves your horse is giving, too. I can tell you a "correct" way, but it helps to see someone doing it when your horse is doing his naughty head shaking.
You can "Google" anything these days and find a book or discussion or video to describe what you want to learn. Why not "Google," "Bridling a horse correctly," on YouTube or another site and see what you find. You will probably see some different techniques. Choose one that works for you. Stay patient and don't give up.
Be sure not to PUSH the bit into the horse's mouth. Offer the bit on your left hand as you hold the top of the bridle with your right hand and when he opens his mouth for the bit (sometimes, tickling the corner of his mouth or his tongue inside the corner of his mouth will help him open his mouth for the bit) let him take the bit and move your right hand with the top of the headstall over his ears. Your right hand on the top of the headstall is what puts the bit in your horse's mouth . . . , and be sure to let the horse open his mouth to drop the bit . . . don't pull the top of the bridle down over his face until he spits out the bit when you move the headstall over his ears to his forehead.
Sometimes, people will put honey or molasses on the mouthpiece to encourage the horse to take the bit. Your horse doesn't need that, but it might help him to let you bridle him until you get more practice with him.
Be safe and keep studying and practicing. Do you have a 4-H Horse Club or any other horse clubs/riding stables near by? That would help a lot.