Cook bacon in a large skillet over medium heat until fat has rendered and bacon is crispy, about 8 minutes. Transfer bacon to a paper-towel-lined plate to drain; leave drippings in the skillet. Add celery, carrot, and bay leaf to the skillet; cook 5 minutes.

Meanwhile, melt butter in a large pot over medium-low heat. Whisk in flour, whisking constantly; cook for 5 minutes. Slowly whisk in 4 cups milk. Bring to a simmer over medium-high heat; simmer for 5 minutes, whisking frequently.

Add bacon, cooked vegetables, potatoes, and corn; return to a simmer, then reduce heat to medium-low. Cook until potatoes are tender, about 20 minutes; add milk as needed to achieve desired consistency. Garnish servings with paprika.