Stay with the horse and become a student of his body language. Don't become angry, impatient, frustrated, or frightened. It's all matter of fact. Unclip his halter from the lead rope and put his halter around his neck for a handle, if needed. Put the bit up by his mouth. If he clenches his teeth, yes, put your thumb or finger in the toothless gum region on his lower jaw, pressing down with firm pressure, as needed. If he raises his head, runs backwards, whatever--do not back off, and do not force the bit. Just stay with him. Keep the bit/bridle in the exact same position relative to his head throughout his entire display. Don't back off, but don't move forward, either, until he realizes that his antics are futile. Repeat as needed, gradually increasing the "pressure" of the stimulus (position of the bit) until he gives in.
(This is presuming there is no underlying physical issues, like horrible dental hooks, or a injury on his head, etc.)