Put the bacon and butter in a medium Dutch oven or other heavy pot. Cook over medium-high heat, turning, until the bacon is crisp, 6 to 8 minutes. Remove to paper towels, leaving the drippings in the pot.
Meanwhile, chop the celery and slice the scallions. Add the celery, rutabaga, potatoes, thyme and all but 2 tablespoons scallion greens to the pot. Season generously with salt and pepper. Cook, stirring, until the vegetables are well coated with the bacon drippings, 2 to 3 minutes.
Pour in the clam juice and 3 cups water, cover and bring to a boil. Open the lid slightly and simmer until the vegetables are tender, about 15 minutes.
Cut the fish into 1 1/2- to 2-inch chunks; add to the pot along with the half-and-half. Cover and simmer until the fish is just cooked through but not falling apart, about 2 minutes; season with salt and pepper.
Divide the chowder among bowls; discard the thyme. Crumble the bacon and scatter over the soup along with the reserved scallion greens. Serve with crackers or rolls.