Cook bacon in a Dutch oven over medium-high heat until crisp. Remove bacon from pan, reserving 1 teaspoon drippings in pan. Crumble bacon; set aside.
Heat bacon drippings over medium-high heat. Add shallot, and sauté 1 minute. Remove from heat.
Bring apple cider to a boil in a small saucepan over medium heat; cook until reduced to 1/4 cup (about 15 minutes). Remove from heat. Add shallot mixture, salt, and pepper. Place cider mixture and cheese in a blender or small food processor; process until smooth.
Combine cabbage and bell pepper in a large bowl; drizzle cider mixture over cabbage mixture, tossing well to coat. Top with crumbled bacon. Serve immediately.