Soak the bread in water until soft and squeeze dry. Blend the tomatoes, peppers, cucumber, onion, and garlic in a large food processor or blender with the olive oil, salt, sugar (if using), vinegars, and bread. Blend until silky smooth (in batches, if necessary) and strain (if necessary).
Add water to the blender/food processor and mix until blended. (If there's no room in the blender, pour mixture into a separate container and stir in water.) Add more vinegar and/or salt to taste hill thoroughly.
Serve in small bowls or tumblers. Garnish, if you like, with finely diced cucumber, tomato, pepper, avocado, chopped hard-boiled egg, or just a drizzle of olive oil.