Biking in the rain won't rust up your ride, but what it will do is wash away the oil on your chain, which can lead to rust pretty quickly. The solution is that you need to oil your chain more frequently if you ride in the rain a lot. Also, fenders help because they reduce the amount of splash hitting your bike when you ride.
To prevent rusting on other parts of your bike, such as bolt-tops or pedals, try applying chain lube or bearing grease.
I kept my bikes outside for many years without a problem (other than theft, that is). If at all possible, look for somewhere to store your bike with an overhang.