I carried/carry a small fleece stuff sack for my fuel canister that I usually use for the Nalgene bottle. It doesn't completely cover the bottle, but the drawstring holds well enough for the job. No bag back-up for leaks, but that's not a bad idea.
Word of caution; depending on which study you believe, the 'boiling' water may leach out little nasties from the Nalgene. Best bet is probably to dump the water in the morning and not drink it, no need to carry an 'extra'.