Preheat oven to 350 degrees F (175 degrees C). Grease an 8x8-inch baking dish.
Stir together the condensed milk, boiling water, and butter in a saucepan over medium heat, and heat until the butter has melted. Place the bread cubes in a large bowl, and pour the milk mixture over the bread cubes. Let the bread sit to soak up the liquid; do not stir.
Beat eggs and sugar together in a bowl until frothy, and add the cinnamon and vanilla extract. Beat the mixture again, and stir in the rhubarb. Gently and lightly stir the rhubarb mixture together with the soaked bread, and scrape the mixture into the prepared baking dish.
Line a roasting pan with a damp kitchen towel. Place filled baking dish on towel, inside roasting pan, and place roasting pan on oven rack. Fill roasting pan with boiling water to reach halfway up the sides of the baking dish.
Bake in the preheated oven until a toothpick inserted into the center of the bread pudding comes out clean, about 1 hour.