Crisp the bacon in a Dutch oven over medium heat, 6–8 minutes; transfer to a plate.
Pour off excess fat, leaving about 2 tablespoons; melt the butter in the pot.
Soften onion and celery in the fat until translucent, about 5 minutes. Stir in garlic for 30 seconds.
Sprinkle in flour and cook, stirring, 2 minutes to remove raw taste.
Whisk in clam juice gradually until smooth; bring to a gentle simmer.
Add potatoes and thyme; simmer partially covered until potatoes are tender, 12–15 minutes.
Reduce heat to low; stir in milk and cream. Do not let it boil.
Fold in clams and most bacon; warm 2–3 minutes. Season with salt and pepper, then garnish with parsley.