Not sure about your device but in my device there is not a file that only has routes. There is a file in the GPX folder on my device named current.gpx that holds the waypoints and routes. When I connect my device to the computer and open BaseCamp the information from the device can be accessed. It is located on the list on the left side of the screen. If BaseCamp can't see your device then you can't send the routes from BaseCamp to your device. You can copy the current file from the device and open it in BaseCamp but I am not sure if you can than copy it back to the device.