I keep the little dimebag that the O2 stone came in over the stone end when not in use as a dust cover. Other than that, I simply sanitize in starsan before each use. One tip is to turn the O2 on before submerging in any liquid so nothing backs up into the stone or line.
I use the bag as a cover too. I don't turn the O2 on before putting in the starsan though. I leave it attached to the hose, stick the end in starsan, turn on the O2 to push any starsan out, put it in the wort for a minute or two, rinse it off, stick it in the starsan, cover it and put it away. Like I said, I've never had a problem. But it seems like most everyone is having success with their procedure as well.
Although now that I think about it, at the brewery it sits in acid sanitizer all the time and only gets pulled out to oxygenate wort. Then it gets rinsed, blown out a bit, and put back in the sanitizer.