Before training on her, I would look at your mechanics of mounting to see if this is something you are causing.
Also, you may have gotten this started by the minute you are seated, you take off. Doing that even at a walk will lead a horse into thinking "foot in stirrup giddy up" and taking off.
Are you making sure you aren't toeing horse in side, are you taking too long to settle in saddle, are you pulling too heavily to the side when mounting, are you dragging your leg over rump?
Does your saddle fit properly, or is it too narrow a fraction and the weight of you mounting is causing it to pinch so she is moving out of protest to that?
There are many things that could be causing this, or aggravating it.
But you also need to teach her a command like "be still" or "stay" and then make her follow that, when leading, haltering, or unhaltering. And when you halter her, don't move out right off, but stand there for few seconds or minutes, that in turn will teach her that she is to wait for your cue.
And once mounted, stay still for 20 counts or more. Don't do any moving at all, that way she is again, waiting for your cues.
Horses make me a better person.