Sneak attack doesn’t work with spells.

Sneak Attack isn't part of this at all. The Bugbear's Surprise Attack feature is a totally different thing.

Here's how it breaks down. Scorching Ray does 2d6 damage with each ray. The Bugbear's Surprise Attack feature adds 2d6 damage to any attack (including spells) against a creature that hasn't had a turn yet, making each ray 4d6 damage in that situation. The 2014 version of the Assassinate ability from the Assassin Rogue subclass makes any hit scored against a surprised creature in the first round of combat an automatic critical, doubling all the damage dice. So, in the situation where you're attacking a surprised creature on the first round of combat, each ray will deal 8d6 damage.

This only works in that specific situation and only using the 2014 version of the Assassin subclass and 2014 surprise rules. Sneak Attack doesn't come into it.

Thx