My mare used to move while mounting.
Your mare might of been really hyper that day... was it windy out? Cold? If she continues to move when mounting try backing her up. As you lift your foot to mount & she moves.. turn around & back her up a few steps. Let her know that if she wants to move YOU will MAKE her move. Eventually she should just give up & stand there because she'll know that if she moves your going to make her work even more.
Give it a try. It might or it might not work. Depends on the horse.