E.D.
That describes my daughter, except that she refused the bottle but did eat some solids.
My solution was to periodically offer her milk and if she wanted it, and stuck with it, she would feed. If she sucked, got distracted, took a little suck, got distracted, etc., I would say, "okay, looks like your not that hungry so we'll try again later," and pack back up.
My daughter is robust and healthy, so I wasn't concerned that she would actually suffer physical damage or risk starving in a few hours.
My milk supply didn't diminish, nor did the gross amount she'd end up eating. It was nice for me, because I was able to keep on with what ever activity we were on.