In 3-quart saucepan over medium heat, cook bacon until crisp, about 5 minutes; remove to paper towels.
In drippings remaining in saucepan over medium heat, cook celery and onions until softened, about 5 minutes. Stir in flour; cook 1 minute.
Add potatoes, clam juice, clams with their liquid and milk. Over high heat, heat to boiling. Reduce heat to low; simmer 10 minutes to blend flavors. Season with salt and pepper to taste. Garnish with bacon. Serve with oyster crackers if desired.