Combine mayonnaise, blue cheese, sour cream, lemon juice, shallot, and garlic in a medium bowl. Mix well, then season lightly with salt and pepper. Cover and refrigerate for at least 3 hours to allow the flavors to develop.
When ready to prepare the salad, preheat an outdoor grill for medium-low heat and lightly oil the grate.
Heat a large skillet over medium-high heat. Saute bacon, turning as needed, until evenly browned and crisp, about 10 minutes. Drain on paper towels. Dice cooled bacon and set aside.
Lightly brush romaine on all sides with olive oil. Season with salt and pepper.
Using a pair of tongs, place romaine, cut-sides down, on the preheated grill. Cook until slightly caramelized, 2 to 3 minutes; it should still be slightly raw and crunchy in the center. Remove to a clean platter and let rest for 5 minutes.
Place each romaine half on a serving plate. Drizzle with dressing and top with tomato and diced bacon.