How did you transition your baby from drinking in a bottle to cup?

My daughter turned 1 a couple of weeks ago and her pediatrician said we should have already transitioned her off from bottles to only sippy cups. Oops. In addition to that we got the go ahead to switch to cows milk. We did the transition to cows milk first and it is going well. She is able to drink 100% cows milk in a bottle. Drinking from a sippy cup is another issue.

We’ve given her a sippy cup (munchkin straw cup) with water since she was about 6 months old. She knows how to drink water from it, but with milk she’ll take a tiny sip and spill it out of her mouth or just push the cup away.

Yesterday we tried to send her to daycare with just sippy cups of milk but she would not drink it. Today I caved in and sent her with one bottle and one sippy. She only took the bottle. She still gets a morning bottle when she wakes up but no night time bottle.

Should I continue the slow transition or just make her go cold turkey? What worked best for you?