Place the chopped bacon in a dutch oven and bring over medium heat. Cook until crisp and then remove to a stack of paper towels with a slotted spoon. Reserve 2 teaspoons of bacon grease in the pot and discard the rest.
Bring the pot to medium-high heat and add the chopped chicken. Stir to coat in the bacon drippings and cook, stirring occasionally, until the chicken is lightly browned. Add the carrots, onions, celery, bay leaf, rosemary, chicken broth and 2 cups of the water and stir to combine. Bring to a boil and then cover and reduce the heat to a simmer. Simmer for 20-30 minutes until the vegetables are tender, but not mushy. Remove the bay leaf.
In a small bowl, mix together the remaining ¼ cup of water and the flour until fully combined into a slurry. Add to the stew and stir to combine. Bring the stew to a boil and cook and stir for about 2 minutes to thicken. Add the salt, pepper and bacon to the pot, stir to combine and then reduce heat to simmer uncovered.
In a mixing bowl, combine the Bisquick and milk and stir to form a dough. Split the dough into six mounds and drop them onto the surface of the simmering stew. Cover the pot and cook for another 15 minutes until a toothpick stuck into the dumplings comes out clean. Taste the stew and add any additional salt and/or black pepper to taste.