Combine tomatoes and next 5 ingredients and 2 1/2 teaspoons red wine vinegar in a small bowl.
Add water to depth of 3 inches in a large saucepan. Bring to a boil; reduce heat, and maintain at a light simmer. Add remaining 1/2 teaspoons red wine vinegar. Break eggs, and slip into water, 1 at a time, as close as possible to surface. Simmer 3 to 5 minutes or to desired degree of doneness. Remove with a slotted spoon. Trim edges, if desired.
Spread mayonnaise on 1 side of each bread slice. Layer each with 1/2 cup arugula, 2 bacon slices, and 1 egg. Top with tomato mixture.