Place tomato slices on several layers of paper towels; cover with additional paper towels. Let stand 5 minutes
Combine mayonnaise, 1 tablespoon basil, and next 5 ingredients in a small bowl.
Spread 1 tablespoon mayonnaise mixture over each bread slice. Top 3 bread slices each with 2 tomato slices, 2 slices bacon, and 1 teaspoon basil. Top with remaining bread slices, coated side down.