Level 18 Wild Magic sorcerers have the following feature (PHB, p. 103):
Beginning at 18th level, when you roll damage for a spell and roll the highest number possible on any of the dice, choose one of those dice, roll it again and add that roll to the damage. You can use the feature only once per turn.
When you score a critical hit with an attack (even a spell attack), you double the amount of dice you roll.
Does the additional damage die from Spell Bombardment also get rolled twice on a critical hit?