Teach her to sidepass, work off leg cues, and move her hind end. When you come around the barrel she should have her nose to it. I will try to find a picture of one of ours doing some training. This horses nose is towards where it should be during training, but he needs to move his butt off a little more. Do a little more lift with your inside rein as you come around. Once they speed up their muscles will have been trained.
Work at a walk first. Walk to the barrel, stop, bend around it, and then walk on...repeat.
Then at a trot. Trot to the barrel, walk, bend around it, trot on...repeat.
Then at a lope. Lope to barrel, trot, bend around, lope on, repeat.
That way when you go full out the horse knows to rate itself right before the barrel, bend, and then go on.
(sorry if you already know this, just thought I would add it.) It's how we pattern ours. :) Good luck.
Pictures might help get some better advice. I am not a really good barrel rider yet. I am learning, but my step-dad trains them and that is how he trains them (and me