jrock18,
It was just 4 years ago that I was in your situation, trying to deal with gun ownership around my college roommates. What's more, my roommates have all been rather peace-loving hippies, who drank and did drugs alot, but did not approve of my owning a gun at all. Suffice to say, this situation CAN be handled...
College dorms: OBEY THE RULES!!! If you're not allowed to have a gun, DON'T HAVE ONE!!! At my school, the college police department had a "check" system, where you could bring your gun to them, and they would check it. You could pick it up from them on your way off campus, and bring it back when you returned. Think, instead of your alternative weapons. Sounds like you've got the baseball bat. Think of some projectile weapons, like mace or tazers. Load up on sharp things. And, increase your warning systems: Set up an alarm on the door, cameras, etc. Plain and simple versions of these things can be purchased pretty cheaply nowadays.
Private Apartments: There are LOTS of ways to secure a gun in an apartment. Design your security around your liability: the roommates. Remember, in our particular situation, we're not trying, necessarilly, to secure the shotgun against theft (or fire, or floods, etc...). We're only trying to secure it against tampering by the roommates. All you need is a box for the shotgun that has a lock on it. The box doesn't have to be hardened ballistic steel, it doesn't have to be fireproof, and it doesn't have to require DNA samples for entry. Just a plain old box with a lock on it! That will keep the drunk college kids from accidentally finding it and messing with it.
My solution, for my handguns, was a nice, decorative wooden chest, with a pretty, yet secure, key-locking brass latch. It works fine. Kids can't get in without the keys, so it's a place to secure the guns, if needs be.
For your shotgun, I would recommend one of the cheap, black plastic gun cases (the kind with the egg-shell foam inside), and a couple of padlocks. The case should have little loops for locks, and that will work fine to keep the drunken college kids out for the night. When it's just you, unlock and open the case, so the shotgun will be handy.
Send me a PM if you want to talk more about it. Good luck!