In a large microwavable bowl, combine Corn Chex, Rice Chex, Wheat Chex, bite-size pretzels, bagel chips (broken into 1-inch pieces), and mixed nuts if using; set aside.
In a small microwavable bowl, whisk together melted butter and Worcestershire sauce until smooth, then stir in salt, garlic powder, onion powder, and everything bagel seasoning.
Pour the seasoned butter mixture over the cereal mixture and toss gently until everything is evenly coated.
Microwave the coated mixture uncovered on High for 5 to 6 minutes, stirring thoroughly every 2 minutes to ensure even cooking.
Spread the Chex Mix in a single layer on a large baking sheet and let cool completely before serving.
Optional oven method: Preheat oven to 250°F. Place the cereal and seasoning mixture in an ungreased roasting pan and bake for 1 hour, stirring every 15 minutes, then spread on a baking sheet to cool about 15 minutes.