It is not forbidden at all.
There is nothing in the torah that prohibits on non-jew from aiding in cooking, or even doing all of the cooking. Most observant jews only require that a jew contribute to the cooking process, and this is purely a rabbinical thing.
Here is how this comes about.
1. To ensure no violation of the laws of kashrut.
As jews are required to keep kosher, and non-jews are not, there is usually worry over whether or not food prepared by a non-jew is actually kosher. This has to do with whether or not the person followed the laws of kashrut in the preparation of the food, and nothing to do with the person themselves. It's assumed a jew would be more inclined to follow these laws han a non-jew....of course this is a huge assumption. Many jews don't keep kosher and wouldn't think twice about cooking your potato pancakes in a pan they just fried bacon in.
So on this end, if the food was to be prepared by a non-jew, a jew would usually be required by the rabbis to supervise. This has turned into a misconception that jews may not eat food cooked by non-jews, or that jews have to be involved in the actual cooking process.
2. Food and socialization go together. The most common interpretation of the Torah holds that jews are not to marry non-jews. To prevent the possibility of a jew and non-jew falling in love, many rabbis simply discouraged the mixing of jews and non-jews in a restaurant setting.
So, you would not be violating anything by having your friend over for Shabbos and having her help with the cooking. What a wonderful opportunity for her to learn about Judaism.