A very common problem with using a bow and drill to start a fire is getting the correct tension on the string. If it is too loose, the drill will not spin, but rather the cord will just slide around it. If on the other hand it is made too tight, and the bow is under pressure, you get the very familiar flying out of the drill. The tension is just so high, that the drill gets spun out and flipped over by the cord. Getting the right balance takes a lot of practice.
There is an alternative method of wrapping the cord around the drill, however, that eliminates this problem. It is sometimes referred to as an Egyptian bow drill.
You start as if you are making a regular bow and brill set. When you have your board and hand hold ready, take the bow, and tie the cord to one end.