Here in the UK we get some of the worse weather conditions as far as rust is concerned: Humidity always between 70 & 100% and regular temperature changes of 10 degrees from one day to another or more between night & day. When the air warms up, it deposits a lot of moisture on any surface that is cold (remember your cold pint of beer). Add to this a dose of salt then you have had it.
The best way to reduce the effect short of putting you bike in your living room would be to make sure it is in a well ventilated place. I would look at putting a fan in the garage to keep the inside & outside temperature similar.
You could buy a dehumidifier for your garage but will have to keep emptying it.
Chains are made of steel so will rust no matter which bike you have