I also went from BFing to cow's milk in a cup. Am trying to think of something useful to tell you, but we didn't really have to go into problem-solving mode as dd was fine about it.
Does your dc have cow's milk on cereal in the morning? To make it a taste she is used to and happy about.
Or maybe have a cup of milk with tea or mid-afternoon, rather than starting with the all-important bedtime feed.
I am sure that having dp do bedtime helped us. I was out of sight and she knows that daddy's boobs are useless so there's no point asking.
We used a proper cup rather than a sippy cup which I think helped.
We also changed the location of bedtime wind-down so she was in her room having a story and cup of milk with daddy on the sofa, rather than in our room which was where I would BF her.
I also remember very clearly that dp and I agreed to give it a go on the understanding that if she cried or didn't like it, I would BF her and we'd try again in a few weeks or when we thought she was ready. I was perched on the edge of the bath, listening in, boobs akimbo, ready to race in and save the day... aaaaand she didn't need me. Hmph.