Coat grill racks with oil and preheat to medium-high.
Combine bison, scallions, salt, pepper, cumin, hot sauce, and cilantro. Form into four 4-inch patties and lightly brush with oil. Lightly coat pepper strips with olive oil and sprinkle with salt. Grill burgers and peppers for 12 minutes, turning burgers halfway through and turning peppers three or four times, until burgers are cooked through and peppers are tender and charred.
While burgers and peppers are cooking, in a small bowl, combine mayonnaise with chipotle pepper and mix well.
During final 2–3 minutes of cooking, place buns, cut side down, on grill and toast. Remove and spread both sides of each bun with mayonnaise. Spread with avocado and top with peppers. Place burgers on top of peppers, and top with lettuce leaves and onion slices, if desired; then cover with bun tops. Serve immediately.