I've not had the baby yet but last winter was my first without a tumble dryer. I've ended up with three clothes airers just for the two of us(!) and normally leave them by the radiator to get clothes dry. The flat (a small one bedroom) can seem like it's packed full of washing at times.
I've just been washing all my cloth nappies to get their absorbancy up before baby arrives and I've found that most of them seem to dry a lot quicker than clothes do, but they seem to take up an awful lot of space on clothes airers. Soooo, what I've actually done may seem a bit weird, but I've filled the baby's room with washing line! One one side of the room is a heavy old wardrobe and on the other is a set of wooden hooks fixed quite high up on the wall. I put a few nails into the top of the wardrobe and a few into the top of the hooks and tied washing line (well actually, just normal string) so there are four lines running across the room. Because of the height they're at and because nappies are only small, there's plenty of space to walk underneath them and the nappies don't drip at all. Once the nappies are dry, I unhook one side of the string and throw it up on top of the wardrobe. I hope baby won't mind!!! I'm also making plans to clear all the rubbish out of our hot water tank cupboard and fill it with shelves - will make a perfect drying room as it's always warm. Another idea I'd consider if our bathroom was a warm room would be to get one of those airers that are on a pulley system fixed to the ceiling so you can lower them to put washing on when you're not using the bath/shower and store it up next to the ceiling when you don't want to use it.
I'd really recommend microfibre nappies as they seem to dry the quickest and bamboo takes forever - I've only got two nappies with bamboo but they both took two full days and a night to dry... and it's summer so I dread to think what it'd be like in winter.