If you have windows, how much of a construction issue would it be to place a fan venters to the outside high on an outside wall? I think any kind of metal will rust based on your past experience until you figure out a way to draw the moisture out of the bathroom.

The reason for chrome plating is because the nickel / chromium plating does not oxidize (rust). Any decent chrome fixture should last 20 - 30 years without rusting.

Try using furniture polish on it. Pledge or something.

Ventilation is key for bathroom longevity - good grade bathroom fixtures shouldn't rust too easily. Don't be averse to simply wiping excess moisture away from your fixtures with a towel - I know its a pain but even the highest quality bathrooms need maintenance :)

There is a product on the market called "Faucet brite" by Gel gloss, this cream base cleanser aids in maintaining the polished chrome finish and avoid corrosion.

Chrome plating over steel is always a problem in a wet environment unless the steel is stainless steel -- which is rarely plated. Always look for chrome over brass. You will pay more for it, but it will last until the sun fades.