Most babies will take a sippy cup from about 4 months, and a straw cup from about 6 months. For those that won't, you can feed them by holding a cup up to their mouth - all babies can feed from a cup from birth, but of course it's more time consuming. Another idea that works for some mums is to put a flannel over the sippy cup and have them suck through the flannel. Sounds odd but I know a few people that's worked with.

Also, as a few posters have mentioned, after the early weeks, babies can go for a few hours without a feed if need be. If you really want to go out, it's fine to do it sometimes and your baby will be ok. It sounds like you are getting past the most dependent phase so hopefully things will be easier for you soon