My S. transitioned without any problems from bottle to sippy at 13 months. With my daughter I thought we'd never wean her from the bottle. If we tried to give her a cup when she was doing the sign for milk, she'd shake her head NO and cry her eyes out. And she definitely knew how to drink out of a sippy cup, because she would drink her water out of a sippy cup no problem. What finally worked was to just do it one day, cold turkey (she was 18 months). She was really mad for a for a few minutes, but I calmly told her that her milk was in there. She'd take a sip and then hand it back and do the sign for milk again, of course she wanted the bottle. I would give her the cup back again and tell her that her milk was in there. It went back and forth like that for awhile but she did finally (rather unhappily) drink some of her milk. The nighttime milk was harder...she's used to drinking some milk before bedtime and was NOT happy about getting the cup again. ;) But I stuck with it - I knew that if I gave in and gave her the bottle it would just make it way more confusing for her. She was pretty mad but again drank some of the milk reluctantly. By the end of the 2nd day we were totally fine.
One thing that may have helped was that I used a certain type of cup for water and a different type of cup for milk.
Good luck!