Or do you buy bottled water for the convenience of saving time rather than saving money?
Kind of both. We buy bottled water for when we are on the go or traveling, but keep refilling the same bottle over and over again with tap water once we get where we are going. We also have refillable containers, but the bottled water is convenient, can be frozen and can be discarded (recyled of course) if it gets dirty.
We have re-usable water bottles (sigg and Kleen ones) for when we go out and about. At home we use those plastic glasses with the straws (look like the re-usable star bucks ones) I found the dollar general here sells them for $2.50 before the cheapest I found was Walmart at $5. So we each have two of those and the kids can only put water in them.