Bottled water is not free. What we dop is take a bottle with us to sip on while checking in and simply refill it from the tap on the ship either in our room or from the water dispenser on the Lido deck. The ships water is as good as any bottled water I have ever had so I see no reason to waste money on bottled water. I am a huge water drinker as well and often buy a bottle when ashore if I feel like it in addition to the bottle I already have onboard. Save all the bottles and simply re-fill them.
Probably not a good idea to refill and reuse plastic water bottles. Once opened and used, bacteria can feast on microscopic food particles, saliva and sweat that are deposited in bottles. If you don't clean and air dry the bottle between refillngs, the tap water you use to refill the bottle is immediately contaminated.