In a heavy 2-quart saucepan, melt the butter over medium-low heat. Stir in the flour. Cook and stir for 1 minute. Remove from the heat.
Gradually stir in the sour cream until smooth. Stir in the beer, mustard, garlic powder and pepper sauce. Heat to boiling, stirring constantly. Remove from the heat and gradually stir in the cheese until melted. Cover and keep warm.
In a large microwavable bowl, toss the shredded chicken with salad dressing. Heat on High power for 2 minutes, stirring halfway through microwaving, until the chicken is hot.
Divide the chicken mixture among the bottom halves of the buns. Spoon cheese sauce over the chicken. Place top buns on and serve immediately with additional sauce for dipping.