Bubble wrap word work fine overall but you need someway to protect the panel itself. Cut a piece of HEAVY cardboard that matches the size of the screen including the bezel and tape it over the screen. If the stand is adjustable I'd use a piece of twine or something to keep it locked in the "down" position. Overstuff the box with peanuts or whatever to keep the monitor as secure as possible in the box.
A little late now but LCDs are one of those things that you should ALWAYS keep the factory package for just for this situation.