In a medium mixing bowl, combine the shredded chicken, mayonnaise, celery, red onion, pickle relish, fresh dill, Dijon mustard, garlic powder, black pepper, and salt.
Stir all ingredients together with a rubber spatula until evenly combined and the chicken is fully coated in the creamy dressing.
Taste the chicken salad and adjust seasoning with additional salt or pepper if desired.
Lightly toast the sliced bagels in a toaster until golden brown and crisp around the edges.
Place one lettuce leaf on the bottom half of each toasted bagel.
Divide the chicken salad mixture evenly among the four bagels, spooning it generously over the lettuce leaves.
Top each serving with the remaining bagel halves to form sandwiches. Serve immediately or wrap tightly in parchment paper for portable meals.