How old is your LO?
I think many people have this difficulty so don't feel alone with her refusing milk from a cup or straw. Mine switched to a small amount in a sippy cup at 12 months but I had to accept it was a very small amount. A month later he took a full bottle worth with a straw in the bottle instead of the teat and I then switched the bottle to a different design (like a toddler or sport bottle as the cup didn't hold enough milk) so I could get rid of all the bottles.
It might help to put a straw directly into the bottle she is used to taking. I split the teats first so he sat upright and drank more quickly (rather than suckling like a baby), then tried a few times with a straw. When he refused I just put the bottle teat back on straight away and got on with the feed. Did this several times over 1 months until he just took the whole thing through the straw. He didn't drink a big full cup of milk until he was more like 2yo+ though so I used a straw for a full year on that one milk drink of the day to keep his dairy intake up. I think for some it helps to see the milk cup/straw/bottle is different from their water cup so they know what is coming.