The bridge probably draws too much power. You will need to get more power to the device. You can do this a number of ways, but the easiest way is to connect a powered USB Hub in between the Xbox and the Device you are trying to use. The USB Hub should provide enough power to the device.
The difference between a regular hub and a powered hub is a powered USB hub has a power supply that plugs into the wall to provide extra juice. A regular hub does not require that you plug it in to an AC outlet.
Side Note: A USB Wifi bridge will not work properly on an Xbox unless you are running some flavor of Linux, because the vast majority of hacked dashboards available for the Xbox do not have the required drivers for most USB devices included in their code.