Bring the water and quinoa to a boil in a small saucepan. Reduce heat to medium-low, cover, and simmer for 15 to 20 minutes until the quinoa is tender and the water is fully absorbed. Set aside to cool slightly.
Add the kidney beans to a food processor and pulse until combined but still slightly chunky. Do not overmix. You want texture, not a paste. Alternatively, add to a large bowl and mash with a potato masher.
Transfer the beans to a large bowl. Add the cooked quinoa, bread crumbs, bell pepper, aquafaba or egg, onion, garlic, cumin, hot pepper sauce, and salt. Mix until well combined. Divide into 4 equal portions, roll each into a ball, and flatten into a patty.
Place the formed patties on a parchment-lined plate or baking sheet and refrigerate for 30 minutes. This allows the binders to firm up and helps the patties hold together during cooking.
Pan-sear. Heat the olive oil in a large skillet over medium heat. Cook the patties for about 4 minutes per side until golden. Work in batches if needed to avoid crowding the pan.
Transfer to toasted buns and add your favorite toppings.