Arrange a rack in center of oven; preheat to 350°. In a small saucepan over medium heat, bring beans, salt, chili powder, pepper, and cumin to a simmer. Cook, stirring occasionally, until beans are warmed through, about 10 minutes. Smash with a wooden spoon, adding more water if needed to help create a smoother consistency, until most of the beans are smashed with some whole remaining; season with salt, if needed.
Meanwhile, arrange tostadas on a large baking sheet. Sprinkle with cheese.
Bake tostadas until cheese is melty, about 5 minutes.
Top tostadas with bean mixture and avocado slices. Drizzle with hot sauce.
