A good way to keep a horse standing still when you're on his back is to keep a horse standing still when you're on the ground.
If she doesn't stand quietly for you when you're just standing there, she's not going to stand quietly for you when you're moving. Horses stand still for us because they're waiting for us to tell them what to do. If a horse moves around, then he's not paying attention to the handler because he's thinking about how much he'd like to move around and get away, not focusing on what the handler wants him to do.
The best way I've taught horses to do this is I teach them what to do when I'm not doing anything, and that's relax. If I tell a horse to back up and he backs up, then I drop all tension and develop a "relax" posture which is resting my hands on top of the training stick, relaxing my whole body and looking calmly at his chest or neck. When they relax, I let them stay that way for about 4 or 5 seconds, then I give them another command like hindquarter yeild, or I lead, then I stop when they do the right thing and I relax. The horse begins to learn when to move and when to relax, and they don't find a reason to move because I tell them what to move and when to move.
If you give the "relax" cue, you should be able to walk around the horse and do whatever you want because you haven't given the horse a cue to do anything else. This means she should stand still while you drink some water, stand still while you text, or stand still while you mount. If I'm standing with a horse and he decides to walk away, then I swing my stick and get him moving until he acts like he wants to stop, then I let him stop. If I'm mounting a horse and he decides to move, then I step down and start lunging him, but I do it quickly. Foot on ground, point and send him off, so he learns to associate moving with doing a lot of work. This reinforces the idea that the horse only moves when you tell him to move, and if he moves without you telling him, then you're going to always make that movement hard work under your command.