Preheat oven to 400°F. Place bacon in a single layer in a cold, large metal pan. Cook over medium heat without stirring until browned on the bottom, about 5 minutes. Stir and cook until crispy, 1–2 minutes more. Transfer bacon to a plate, leaving the fat in the pan.
Use a serrated knife to trim the crusts off the bread. Cut each slice into 4 triangles.
One at a time, dip one side of each bread triangle into the reserved bacon fat. Place on a baking sheet, bacon-fat side up.
Bake toasts until edges are crisp and lightly golden, 4–5 minutes.
Meanwhile, mix mayonnaise with ½ teaspoon salt and ¼ teaspoon pepper in a small bowl. Cut lettuce leaves in half lengthwise, then tear each half into 2-inch pieces. Slice tomatoes crosswise into ¼-inch rounds and season generously with salt. Slice avocado lengthwise into ¼-inch strips.
Spread about 1 teaspoon seasoned mayo on each toast. Top with a piece of lettuce, a slice of avocado, 2 bacon pieces, and a tomato slice, shingling as you go. Finish with a pinch of pepper.