Cook bacon in a large skillet over medium heat until crisp, about 5 minutes.
Remove bacon to a plate; pour off about half of the bacon grease. Stir carrots, celery, and bay leaf into the same skillet; cook and stir vegetables until slightly softened, about 5 minutes.
Melt butter in a large pot over medium-low heat; whisk in flour. Slowly whisk in milk, bring to a simmer, and cook, whisking frequently, until slightly thickened, about 5 minutes.
Crumble bacon. Stir bacon, potatoes, corn, paprika, and vegetable mixture into milk mixture. Simmer soup over medium-low heat, stirring frequently, until potatoes are tender, about 15 minutes.
