Re: EBF, won't take bottle, introducing sippy cup?
I'd actually avoid bottles, sippies, and solids right now. They would all decrease your baby's dependence on the breast, and that could rapidly turn into a full-blown nursing strike instead of simple (but frustrating!) distractibility.
Have you tried taking baby to nurse in a calm, dimly-lit location? A dark bedroom is where a lot of moms with distractible babies choose, or are forced, to nurse.
Coolest thing my big girl said recently: "How can you tell the world is moving when you are standing on it?"
Coolest thing my little girl sang recently: "I love dat one-two pupples!"