for transporting coral, depending how big you can get away with the Styrofoam boxes. if attached to rock, i would say a regular UNSCENTED bag in your bucket to protect from scratches should suffice. temperature is more important though. make sure its stable and within range.
And I'll add that the list of "toxic items" also includes bleach. I wiped out one of my tanks after using a container that had fresh bleach residue in it during a water change, and I didn't notice until after the damage had been done.