Preheat oven to 450 degrees. Separate asparagus into bundles of 3 stalks each. Carefully wrap a piece of bacon around each bundle, starting about 1/2 inch from the bottom of the tip; secure with a toothpick. Transfer bundles to a rimmed baking sheet. Drizzle with oil, and sprinkle with 3/4 teaspoon salt; season with pepper. Roast, flipping halfway through, until asparagus begin to wilt and bacon is brown, 20 to 22 minutes.
Meanwhile, whisk together mayonnaise, chili sauce, lime juice, cilantro, and 1/2 teaspoon salt in a small bowl; season with pepper. Sauce can be refrigerated in an airtight container up to 1 week.
Transfer bundles to a platter; remove toothpicks. Serve with dipping sauce.
To keep the bacon from unraveling during cooking, wrap a slice snugly around the middle of the asparagus bunch. Insert a wooden toothpick through the bacon and stalks to secure.