My daughter initially refused as well.
I started giving her a bottle in the morning and at night only. During the day I would offer her her sippy cup and no bottles at all. The first couple of days she would drink only a little, I'd give her about a half-hour and then put water in her cup instead. She would drink the water easily. After about three days she started drinking the milk out of the cup. Once she did that, I waited another couple of days and took away the morning bottle and then finally a few days later the night time bottle. I noticed with her it was very important that the sippy cup with milk was the first thing I gave her when she woke and when she was hungry. She was much more willing to drink it.
Also, the type of sippy cup makes a huge difference. She would only use Dr. Browns or Tommy Tippie. The first couple brands I tried she refused. A few friends of mine noticed that once they found the right brand of sippy cup, many of whom use one of the two I listed, it made it much easier to transition.
Hope this helps!