I wasn't aware of kiln-dried aspen, but I was of kiln-dried pine. A local rat breeder instructed me that kiln dried bedding typically does nothing more than remove moisture from the wood and doesn't actually get hot enough to remove phenols, which I assume goes the same for fungi and bacteria.
That same person also says aspen is safe so long as there is no excessive odor or dust. She is against pine and cedar, whether or not they were kiln-dried.
EDIT: I've never used any sort of wood bedding for my rats. I've always used paper or fleece, so I'm not sure if any of this is true or not. Perhaps more experienced members could give insight on this.