Actually, depending on how you look at it, radiation could work...
Anthrax is bacterial. High doses of radiation would kill the bacteria. But if she's invulnerable, the radiation wouldn't harm her. You'd need a high dose, but we know that Superman can handle that. He's walked into the reaction chamber of a nuclear power plant, been hit with a small atomic blast, and... he's flown right up to the edge of the sun. Which might be the best option here. There's a lot of hard radiation in space, and more that's produced by the sun (which is, after all, a giant nuclear reactor). Particularly solar flares. It's radiation that would strengthen a kryptonian, but would kill most Earth-based life. Including bacteria.
Of course, the bacteria are inside her body, which could, depending on how you define the power, mean that they're within her aura of invulnerability. Which makes them much harder to kill.
