Lay bacon in bottom of a cold, large stockpot or Dutch oven. Turn heat to medium and cook until bacon is crisp, turning often. Remove and set aside on paper towels.
Add butter to pot and melt. Add celery, onion, garlic, and thyme. Season well with salt and pepper. Cook, stirring occasionally, until vegetables are soft, about 15 minutes. Add white beans, stock, and coconut milk and bring to a simmer. Cook for 10 minutes, stirring occasionally.
Purée soup with an immersion blender or by transferring to a food processor or blender. Adjust seasonings to taste. Serve with cooked bacon crumbled on top and thyme garnish.