In a small bowl with a fork, smash together butter and 2 tablespoons bleu cheese crumbles; set aside.
For the burgers:
In a mixing bowl, stir to combine ground beef, 1/3 cup bleu cheese crumbles, bacon pieces, and steak seasoning. Wet your hands to prevent sticking and shape into 4 patties slightly larger than the buns. Cover with plastic and set aside in refrigerator.
Set up grill for direct cooking over high heat. Brush and oil grate before cooking. Salt and pepper burgers and place on hot grill. Cook for 4 to 5 minutes per side for medium. Serve hot on toasted onion roll. Spread with bleu cheese butter, lettuce, tomato, onion, and sliced avocado, if using.
INDOOR: Follow instructions for preparing burgers. Preheat broiler. Place burgers on wire rack over foil lined baking sheet or broiler pan. Broil 6 inches from heat source for 4 to 5 minutes per side for medium.