For the sauce: Stir up the sour cream, horseradish, mustard, chives, dill and garlic in a small bowl and adjust salt to taste.
For the burgers: Arrange the bacon on wire-rack-lined rimmed baking sheet or slotted pan. Bake until very crisp, 12 to 14 minutes.
Combine the beef with grated onion, salt and pepper and Worcestershire sauce and score into 4 portions. Form 4 patties of the beef mixture thinner at center than edges for even cooking. Cook patties in a little oil, about 7 minutes, turning occasionally. Then melt 2 slices of cheese on the patties for a minute or so.
While the patties cook, toast the English muffins. Lightly butter bottoms and add thinly sliced dill pickle chips.
Place burgers on buttered side of muffin and top with 3 half-slices of bacon, watercress and horseradish sauce.