Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Transfer bacon slices to paper towels. Drain excess grease from the skillet.
Crumble 4 slices bacon into the skillet. Add onion, celery, garlic, and thyme; cook and stir over medium heat until soft, about 5 minutes.
Transfer bacon mixture to a large pot. Add corn and chicken broth. Bring soup to a boil; cook until flavors combine, about 5 minutes.
Pour 2 cups of soup into a blender. Cover and hold lid down; puree until smooth.
Return pureed soup to the pot. Stir in half-and-half, pepper, and salt. Bring to a boil. Stir in shrimp; cook until shrimp are opaque, 3 to 4 minutes.
Ladle soup into bowls. Crumble remaining 2 slices bacon on top.