Peel the bananas and place them in a blender with the vanilla pudding and milk. Blend until the mixture is smooth.
Pour the blended mixture into four popsicle molds or small paper cups. Insert one popsicle stick into the center of each mold.
Freeze the pops for at least two hours until they are solid.
Once frozen, remove the pops from the molds. In a microwave-safe bowl, combine the white chocolate chips and coconut oil. Heat in 20-second bursts, stirring between each, until melted and smooth.
Drizzle the melted white chocolate over each pop in a crisscross pattern to create the look of mummy bandages. Press two candy eyes onto the chocolate while it is still soft.