Using an insulated bottle kind of defeats the purpose which is to transfer heat from the water to yourself. You'll wake up in the morning with a bottle full of hot water but you'll still be cold.
Kleen Kanteen sells non-insulated metal bottles as well; I've used them for this purpose (not sleeping, but holding against my body to help stay warm in a cool room). Bonus: once the temperature drops far enough you can also drink it for a quick internal thermal boost, if needed.