Finely dice the onion and place in small bowl with water. Microwave for 1 minute, let cool, then drain.
In a bowl, mix together ground bison (or beef), cooled and drained onion, salt, pepper, Worcestershire, soy sauce and steak sauce. Using your hands and a light touch, combine thoroughly. Shape into six ¼-pound patties, round and an even thickness. If making ahead, wrap and refrigerate for up to a day.
Set a nonstick skillet over medium heat. Fry burgers in batches, if necessary, until desired degree of doneness, about 5 minutes on the first side, 3 minutes on the second for well done. Remove from skillet and drain on paper towels. (If you have a grillmeister in the house, by all means, grill the burgers.)
Toast the buns and assemble sandwiches: spread bun with mayonnaise, add patty, then cheese, then pickle.