When I went through this with my son I went cold turkey. I told him we had to give the bottles to another baby that we knew and he had to start drinking out of a cup. So a little lie, but it helped. I let him pick out his new 'milk cup' and 'water cup' at the store (he ended up choosing princess theme cups) and that was what he got to drink his milk out of at night. It took two nights before he accepted not having bottles. When he asked for a bottle I would remind him we gave them away, but that he could have his new milk cup or water cup in bed. So now that's what we do. And I only put enough in that he'll drink before sleeping and not having any leftover in the morning. Most cups come with those plugs to keep the liquid from coming out easily, so that should help in your situation.
Good luck.