Preheat oven to 350°F Sauté bacon in wide ovenproof pot over medium heat until crisp. Transfer bacon to paper towels.
Sprinkle rabbit with salt and pepper. Increase heat to medium-high. Working in batches, add rabbit to pot and sauté until browned, turning often, about 10 minutes per batch. Transfer to large bowl. Add 1 tablespoon butter to pot; add onion, carrots, and celery. Sauté until vegetables begin to brown, about 10 minutes. Add garlic, thyme, and bay leaves; stir 1 minute. Return rabbit and bacon to pot. Add wine; simmer 5 minutes. Stir in broth and tomatoes; bring to boil. Cover pot tightly. Transfer to oven and cook rabbit until very tender, about 1 hour 15 minutes. Season with salt and pepper. Divide among plates; spoon grits alongside.