Heat the cranberry juice in a small saucepan over high heat. Whisk in the cranberry sauce and heat until mixture is completely melted and a pourable consistency is reached. Remove from the heat and allow to cool to room temperature.
Heat the milk in a small saucepan over medium-low heat until to just before it comes to a simmer. Put the white chocolate chips in a medium bowl and pour in the hot milk. Let sit for 1 minute then whisk until smooth. Refrigerate until chilled but not set, it should have a thick but pourable consistency.
Add the cream to a chilled medium bowl and beat with a hand mixer or whisk until stiff peaks form. Add the white chocolate to the whipped cream and gently fold together until completely incorporated.
Spoon about 1 tablespoon of cranberry sauce into the bottom of 4 dessert glasses. Put mousse into a resealable plastic bag and snip 1 corner. Use the bag to pipe mousse filling between the 4 glasses. Chill for 2 hours and up to overnight. Just before serving, top with a drizzle of remaining cranberry sauce.