My finished horses will pick a spade up and carry it without a headstall. When they are colts, I just stick two fingers in their mouth and they open. Then I pop the bit in and follow up with a lot of praise. I do this repeatedly, and they eventually just open their mouth when they feel the bit at their lips, just like Smrobs stated. You just have to be careful not to ram it in their mouth or drag it across their teeth, they will eventually take it willingly, the carrot chunk trick works, unless you have a bit with a complicated mouthpiece. The first time you have to dig carrot out of the hood on a Mona Lisa, you won't use treats again. Lol. Good luck!
~Started young horses in Bosca te Ador, unto the two rein the old Spanish spade, brought them along with two hands that were gentle. Some fine reining horses as ever were made~