my bb loves to drink water and diluted fruit juice etc but she will only drink it from her cup (Combi cup wit the straw - strongly recommended). She could hold the cup by herself when she was around 9 months old. But for her milk, she will only drink that from the bottle. Like your bb, she also went through a phase when she did not like her milk. So I tried to put it in the Combi cup but she refused. Even now she is 16 months old, her water must be in the cup and her milk in the bottle. The other way round and she refuses to drink.
Babies are very funny - they each have their own characters. My experience tells me that you just have to keep trying different methods eg try a different cup, try a different nipple or bottle, try letting baby get more hungry before giving the water, give the water after bb has eaten some biscuits ie when her/his mouth is a little bit dry
One last tip, you could try to give bb Wildalps Spring Water which is water especially made for babies, it comes from Austria and my bb loves to drink it. My paediatrician recommended it - he says that some of his bbs will only drink this type of water.
My BB also like that from 4 months. But, he will drink milk when he is fell in sleep. We also have used spoon to give him milk when he is unleep. Just last for 1 months, then he don't like it. And, now we use syringe to pump him milk. He like it.