Let me admit that I am answering this more from the position of a former Chemistry teacher than a cook. I never encountered this type of question as a professional cook, but I certainly did as a chemist. So please forgive the somewhat scientific answer.
The primary concerns in storing baking powder are keeping it dry and cool. Exposure to air in itself is not a big concern, but it's best to keep it in a reasonably air-tight container to prevent moisture in the air from effecting the baking powder.
The way baking powder works, is (primarily) by a reaction between the main ingredient (Sodium Bicarbonate), and a secondary ingredient which is some kind of acidic salt (often Sodium Aluminum Sulfate) when they combine with water and heat. A lot of fancy chemical "stuff" happens that you probably don't care about, that ultimately produces a byproduct of carbon dioxide - a gas. The gas causes tiny bubbles in the batter or dough and gives it a softer texture.
So if you want to store baking powder for a long time, you must protect it from water and heat. If you are ever in doubt about the viability of your baking powder, I'll suggest a simple test. Add a small amount of baking powder (1ts/5ml) to a small amount (2oz/50ml) of hot water. If the baking powder is still viable, it should become effervescent and produce small bubbles or fizz in the water. This tells you it will do the same in whatever you are baking.