I prefer to chill the bottle gradually, if possible.
Going from room temp (or higher, heaven forbid!) only to be plunged into an icey cold bucket can "bruise" the champagne, and make the complexities go "dumb" - I have tried this, and felt I could taste a difference, though I will be the first to admit my test procedures were hardly scientifically rigorous.
Best serving suggestion in my experience is to keep the bottle on ice throughout the drinking session, pour smallish amounts into the flute, and let it warm up a few degrees in glass from the icey temps of the ice/water bucket.
You'll find many more complex and rich flavours develop this way.