I have a special hate for bungee cords, because my brother nearly lost an eye to one (thanks to some great surgeons, he can still see). Bungee cords suck, plain and simple. They are not a reliable tie-down, and there is no situation for which there isn't a better solution.

My favorite alternative is a simple cam strap: nylon strap with a cam at one end. These are used a lot by whitewater rafters and other whitewater boaters, because they make such a great, versatile tie-down when you're transporting boats. The NRS straps are sort of the industry standard -- very rugged and last for years and years. Simply wrap the strap around the rack and the object to be secured, however many times is appropriate, cinch tight, and wrap up any slack (best way to do this is to tuck the end under the next-to-last loop, then pull it tight). If it can hold a pile of kayaks on a car going 70 mph, it can hold whatever you're carrying on a bicycle rack.