@Xzayer, Think of travel flasks. Just like homemade-bentou box, it's not unusual in Japan (perhaps in Asia as whole) for students to also bring their own waterbottle from home, usually to not only cut cost on daily pocket money but also to discourage buying and drinking less healthier softdrinks and the likes.
If what confused you is why the little sister even need to borrow the bottle, well i had no idea too.