To dry out containers quickly that have a long neck (Example: vase or a lotion bottle) do the following:
Take some alcohol that you would buy in the drug store. Poor a small amount into the bottle that you want to dry out. It's ok that you still have water in the bottle, droplets i.e., Swirl the water around to get the entire area covered inside the bottle; drain! Put in dish strainer upside down to dry - the drying time is cut in half because the alcohol on the side/bottom of container will evaporate and your drying time will be cut in half. It really works! Try it!