Heat the diced bacon in a soup pot over low heat. Add the onion, celery, thyme, and bay leaf, turn the heat up to medium, and cook until the vegetables are soft, about 10 minutes.
Dice the potatoes and add them to the soup pot with the clam juice. Simmer until the potatoes are just tender, about 10 minutes. Add the milk, peppers, salmon, and dill, and cook until the salmon is just cooked through, about 10 minutes. Remove the thyme and bay leaf. Adjust the salt and pepper to taste.