While 'di + la' = 'della' does mean 'of the (feminine)', I believe the usage of 'della' in this sentence is 'some'. It isn't being used as a possessive article to make the bottle the subject, it is merely stating that there is a quantity of water in the bottle.
"la bottiglia ha dell'acqua" translates to "the bottle has some water (whether or not you append 'in it')" as opposed to 'no/plenty of water' etc.
"La bottiglia ha dell'acqua" I am wondering if this sentence will be said the same way by a native Italian! Also it is my feeling that "The bottle has some water" it is not a good sample of possessive! Don't you have to add an apostrophe to bottle to make it work? ( The bottle's water ) This translates to "L'acqua della bottiglia" Any comments?
It is strange that bottiglia means bottle here and a hundred other times, but in another example bottiglia was not accepted as bottle. It was translated as glasses or cups. In my upcoming trip to Italy I wonder what I will get when I ask for a bottiglia dell acqua. That preposition is probably wrong bu t what the *****