I had the same in 1st year uni halls – third floor flat, no bikes allowed.
I used to take the wheels off, put them in the wheel bags and store them under the bed, the rest went into a big bike bag and I just chucked a towel over the lot.
I could wipe the worst of the mud off it outside, the rest I’d let dry then brush it off in the kitchen and sweep it up. Initially my housemates complained but then they realised that it was the only time the kitchen floor ever got swept. 😉
Road bike was easier, I just took the wheels off and stored it under my desk – push the chair in and it was all but invisible at room inspection time.