I have well water. Wouldn't give distilled nor bottled water to my pets. The amount of things like arsenic and lead are so teeny as to be unimportant. There's more naturally occurring "contaminates" in the air in a common home than would be in a serving of water.

And bottled water goes through a process similar to most tap water. It isn't someone dipping that bottle into a pure free flowing spring. It's pumped into a factory that runs it through filters and into holding tanks and finally into bottles. All those pipes and hoses and equipment? Same sort that is in most municipal water facilities.

I'm not saying you're WRONG to use bottled water. I'm saying you probably don't NEED to. But if you feel better giving bottled water, go for it. I used to drink from a hose, and even drank right out of the river, puddles and pools. I barely twitch and my head only falls off on rare occasions... lol.

I can't see that distilled water would be "bad", but I don't think it would be "good" either.