Place the salt cod, milk, and bay leaf in a medium heavy-bottomed saucepan over medium heat and bring to a light simmer. Continue to simmer for about 10 minutes until the cod flakes easily.
Remove the pan from the heat and allow the cod to soak in the milk as it cools to room temperature, about 30 minutes. Discard the bay leaf.
Combine the celery, bell pepper, and parsley in a medium stainless-steel mixing bowl. Using a fork, flake the cooled salt cod in bite-size pieces into the bowl with the vegetables; stir well to mix. Dress the salad with the olive oil and lemon juice. Toss, then season with salt and pepper. Serve chilled.
Recipe courtesy of My Italian Table by Ron Suhanosky/Kyle Books, 2011.