Spread the pizza sauce over each bagel half, right to the edge.
Pull the string cheese apart into thin strips. Lay them across the bagel in a random crisscross, leaving a small gap about a third of the way down where the eyes will go. Thin strips are what make this look like bandages instead of a pile of cheese.
Trim any cheese hanging over the edge with kitchen shears.
Press two olive slices into the gap for the eyes.
Set the bagels on a baking sheet and bake about 10 minutes, until the bagel is crisp and the cheese has melted. Pull them before the cheese browns so the bandages stay white.
Notes
Assemble these a few hours ahead for a party, keep them covered in the fridge, and bake right before serving. Baking early and reheating is what makes them soggy.