Hi!
Although I haven't been in your situation, I'll try to give a little bit of advice based on what I've experienced. I found that my DD's took a fair while to get used to the sippy cup (didn't really cotton onto it properly until about 10-12 months) whereas bottles they were fine from the start. I know some people find it difficult to get their babies onto bottles too. So what I'd suggest is introduce both. See which one she takes to the easiest and that may be your answer. There are some negative things going around about bottles after 12 months of age because of their teeth etc, but I don't think there's anything wrong with them prior to 12 months. If you're using EBM, then I can't imagine it would affect your supply. HTH!