First off welcome to the forum. We would need more information than what you posted. When you are riding, where do you ride her? You guys alone in a field? Arena? Or is this happening on the ground? How much training has she had? What do you try to do when it happens?
The more information we get, the easier it is to figure out what it is we can try to do.
I'd like to know if you are loungeing her. I have Arabians exclusively and there is a reason they have the rep that they do. Sounds to me like she needs more ground work period, but I always lounge before a ride. It not only "takes the edge off" but it is a great oppurtunityto assess your horse for lameness and mood. Also, does she seem like she is taking off for fun becuase she enjoys the freedom of an open field, or does she seem afraid?