First off, you don't need a new bit. Just do a simple excersize to improve the brakes. Say whoa, melt your hips back an use your seat to stop, and if she still isn't stopping touch her mouth and make her back up. Eventually she learns that if she stops when you say whoa you won't touch her mouth.
As for catching, don't play games with her because she is playing games with you. Dont give her treats unless the halter is on. Dont hide the halter. Walk forward with a purpose an body language that says "I'm gonna catch you" and if she runs off, just follow with the same posture. As soon as she stops and looks at you/puts her head down she is tellin you she wants to stop playing. Quit advancing and turn away from her. Give it a minute, and then just slowly move toward her....relax your shoulders, keep your eyes down. And when you get to her, slip the halter on and then if you must, give her a treat or a scratch. If she runs away again, follow with the same firm posture that you were doing before.
Teaching a horse is about pressure and release. It doesn't matter if it's mental or physical pressure. In this case, it's mental. When you follow her you have your eyes up and are applying pressure. By turning away when she does good, you are releasing the pressure. It is critical you make the differance in body language, an never praise unless the halter is on.
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