I've never worried about humidity here in Chicago where it is very humid in the summer and very dry in the winter. I always just went with the fact that a cork that is wet from the inside (wine) is good enough. I think at normal humidity levels that is most likely true.
However, I spend a lot of time in Colorado and I know that dryness there is an entirely different thing! In Colorado I would be concerned about a lot of ullage as I suspect the humidity gradient between inside and outside of the bottle is enough to cause problems over time. I think some sort of passive humidification is probably fine, like you suggest- a bucket of water or a big pan. An active humidifier would probably be even better, but who wants to add water to their wine cellar every day? If I was building a cellar in CO I would consider using loose rocks (like pea gravel or small river rocks) as the flooring and just dousing it in water every so often. The wet rocks have a large surface area and will allow for evaporation pretty readily. I know that mold is really not a concern in CO, which is quite different for those of us from wet parts of the world.