It doesn't really eat the nuclear waste, it "just" feeds on the radioactive energi, so it doesn't speed up the decay. But you can use them as a radiation shield.
As far as I know you cannot speed up the decay, unless you put it in a particle accelerator and bombard it into something with a much faster half life?
That just gives you radioactive bacteria who might crawl around a bit and spread the radioactivity. You can't get rid of a nuclear problem by chemistry.
You are correct, of course, but in a sci-fi scenario maybe you could have a colony of fungi that move nuclear material around internally to keep it 'hot', thus 'burn it off' faster to extract energy. It might collect material from a wide area.
One mode of radioactive decay is electron capture, which is absolutely impacted by temperature (just mentioning this as trivia, I meant hot-as-in-radioactive).
Moving around radioactive material doesn't affect its activity, unless you're specifically talking about collecting it into a near-critical mass or something like that. Presumably that's what GP was thinking about wrt neutron reflectors. And I'm pretty sure that only works even in principle if the isotope in question can be stimulated into activity by absorbing neutrons (or other radiation I suppose), which is not the case for all of them. Bio-accumulating a critical mass of radioactive material ion by ion... well, it sure is sci-fi.
Things happily eat nuclear waste. This is one of the big problems with nuclear waste, your body will happily integrate radioactive isotopes or heavy metals, which then slowly kill you.
