To make the salad dressing, place the mayonnaise, sour cream, ⅓ cup bleu cheese crumbles, 1 tablespoon chopped chives, Worcestershire sauce, lemon juice, rice vinegar, milk, black pepper, and salt in a medium bowl.
Stir to combine the dressing, cover, and refrigerate until ready to serve.
Place bacon in a large skillet over medium heat.
Cook the bacon until crisp and, using a slotted spoon, remove the bacon from the skillet and set aside to drain on paper towels. Reserve the pan drippings in the skillet.
Thoroughly pat the onions dry with paper towels.
Add the olive oil to the skillet with the pan drippings and whisk to combine (you want about ½-inch of oil in the skillet, add additional oil if necessary). Heat the oil and pan drippings over medium heat until the temperature reaches 300 to 350 F.
Once hot, add the sliced onions in batches, and fry until golden and crisp, about 2 minutes.
Using a slotted spoon, remove the fried onions from the oil, and set aside to drain with the bacon.
To assemble the salads, divide the iceberg quarters between plates.
Generously top the lettuce with dressing.
Top with the halved cherry tomatoes, the remaining ⅓ cup of bleu cheese crumbles, and the bacon.
Sprinkle with the fried onions and remaining 2 tablespoons of chives before serving. Serve with any remaining dressing on the side.