A.L.
Shower caddy.
Dorm supplies are abundant right now, so you should be able to find a cute one.
Mine has glass cleaner, a couple of swiffers, an extra trash bag, some Pledge, a coule of paper towels, a couple of old socks, an old toothbrush (for scrubbing small spaces), and a timer.
Each bathroom also has a bottle of toilet cleaner, a toilet brush, and a canister of Lysol wipes. (The kitchen also has a canister of wipes, and extra baking soda.)
The timer is for my "five minutes per room" plan. Walk into a room, and set your timer for five minutes. Do everything you can. When the timer goes off, finish the task you are currently on (ie, don't leave the bathroom mirror half wiped or the desk half dusted or whatever), and move on to the next room. Pick ONE room to focus on in a deep cleaning. I find it makes the cleaning a lot less tiresome, when I know I only have to do it for 5 minutes at a stretch. You can do anyting for 5 minutes. (And you'd be surpirsed how much you can do in 5 minutes, too! Depending on the room, I also bring a small bin for "Things that don't belong in this room." When the timer goes off, I re-distribute the stuff into their proper rooms.)