The more I look at this item, the more I'm convinced it's not a rolling pin. I think it might be an automobile vase.
In the glory days of motoring before WWII - especially in Pierce Arrow automobiles and the classic Rolls Royce models, cars had vases that sat in special holders inside the "carriage" of the vehicle. Usually, the glass vase was placed in some sort of holder that was attached to the interior frame. The holder could be brass or highly polished wood. A flower or two or three were placed in the vase in water. Every vase I've ever seen in a Pierce-Arrow has a narrow, nipple bottom.