Preheat an outdoor grill for high heat and lightly oil the grate.

Combine bison, bread crumbs, egg, Worcestershire sauce, hot sauce, garlic, and pepper in a large bowl. Form into 4 patties. Place patties on a baking sheet. Cover with foil and refrigerate until chilled, about 15 minutes.

Spray patties with cooking spray. Cook on the preheated grill until hot and slightly pink in center, about 5 minutes per side. Top each patty with cheese slices. Continue cooking until cheese melts, about 2 minutes more. An instant-read thermometer inserted into the center should read 160 degrees F (70 degrees C).

Sandwich patties between toasted bun halves and serve.