Combine bell peppers, onion, mushrooms, olive oil, and seafood seasoning in a large bowl. Stir until evenly combined. Set aside while you preheat the grill.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Place boudin directly on the grate. Place vegetable mixture in a grill basket. Grill for 5 minutes. Turn boudin over, stir the vegetables, and cook until an instant-read thermometer inserted into the sausage reads 160 degrees F (71 degrees C), about 5 minutes more.
Place boudin in hot dog buns, top with mustard, and serve with vegetables.