I am sensitive to water issues and I have trouble with water everywhere (even going from Toronto to Florida!). Surprisingly, I had no problems at Desire and I too drink a lot of water - learned that lesson the hard way
Taking the empty bottle from your room is a good idea. It is less likely to get spilled or get sand in it when in the bottle. Have them fill it at the bar for you.
Also, when we were there last May ('08) there was Grey Goose available at all the bars for no additional charge...not sure if that has changed recently but it was great last year.