Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon slices on paper towels; reserve bacon grease.
Mix bison, bread crumbs, egg, Worcestershire, salt, and pepper in a bowl until evenly combined. The mixture should be slightly sticky and easy to form. Split into 4 equal patties. Use some leftover bacon grease to moisten each side of the patties; this will inhibit them from sticking on the grill and adds a little flavor.
Cook patties on the preheated grill until browned, about 5 minutes on each side. An instant-read thermometer inserted into the center of each patty should read at least 160 degrees F (70 degrees C). Place Cheddar slices on each patty and continue to grill until melted, about 1 minute more. Remove to a plate.
Place buns on the grill, sliced sides down, to toast, about 1 minute. Spread mayonnaise over the toasted buns. Add burgers and bacon.