1. Place racks in uppermost part and middle of oven and heat to 400 degrees. Line a baking sheet with foil and set aside.
2. Combine chicken, 1/2 cup barbecue sauce, and salt in a medium bowl and toss to coat; arrange on prepared baking sheet. Transfer baking sheet to middle rack of oven and bake until thickest part of chicken registers 165 degrees, 30 to 35 minutes. Move chicken to upper rack and broil until sauce has caramelized and darkened in spots, about 5 minutes. Remove from oven and let rest 10 minutes.
3. While chicken is resting, whisk buttermilk, mayonnaise, and remaining 1/4 cup barbecue sauce in a medium bowl until smooth. Divide lettuce among four bowls and top evenly with pinto beans, corn, tomatoes, avocado, and tortilla chips.
4. Slice each chicken breast across the grain into 1/2"-thick slices and arrange over salads.
5. Drizzle with dressing and serve immediately.