Preheat oven to 400 degrees F (200 degrees C). Line a baking sheet with foil, and place a baking rack on the foil-lined sheet.
In a bowl, mix together the condensed milk and mustard until thoroughly combined. Cut the crusts off the bread and discard crusts or save for another use. Roll a slice of bread out flat with a rolling pin. Place 2 pieces of bacon down onto a work surface, side by side, and lay the bread slice on top of the bacon. Spread about 1 tablespoon of the milk-mustard mixture over the bread. Sprinkle about 1 tablespoon of Cheddar cheese in a line down the center of the bread.
Roll the bacon and bread into a firm roll, working from the short ends of the bacon so they wrap horizontally around the roll. Secure the roll with a toothpick. Repeat for remaining ingredients. Place the bacon rolls onto the baking rack over the pan.
Bake in the preheated oven until the bacon is crisp and brown, about 20 minutes, turning the rolls over once or twice during baking to crisp the bacon uniformly.