Don't need to dry it if its coming out of salt water. We put our school kites away wet with salt water all the time.
However, coming out of fresh water, you should dry it, or it can mildew.
I think this works for schools who will fly their kites regularly, but doesn't work for me. I heard this enough that I stopped drying my kites after salt water sessions, but then I'd still get mildew stains after storage. I think the issue is if you leave them stored up long enough, the salt water will cause non-salt water condensation elsewhere and that will stain. Anyway, that's just a guess, but I know if I store it salt water damp for a week or two, I get stains.
I have garage access, but just drape it over a line and have a fan moving air across the kite. It is dry by morning. Since there isn't a breeze blowing it around the rope doesn't wear the kite at all. I'm sure you could do the same thing inside your apartment... (run a line, blow a fan to keep the air moving)