Heat the olive oil in a saucepan over medium heat. Stir in the garlic, bell pepper, and onion; cook and stir until the onion has softened and turned translucent, about 5 minutes. Stir in the blue cheese, cream cheese, heavy cream, and milk. Heat until the cheese is melted and the mixture is simmering, 5 to 7 minutes.
Stir in the diced tomatoes, tomato juice, basil, sweetener, and pepper. Continue to cook and stir until the soup is heated through, 15 to 20 minutes.