There is no distilled water available for sale on board. What I use to transport mine is a Rubbermade 1 liter container. They are well made, can be sterilized are easily carried and only costs about $1 at Wal-Mart. It fits easily in my carrying case.
If you absolutely had to have distilled water you could get it in the infirmary but it would have to be an emergency and just enough for one night. So you must bring your own.