Better way to do laundry?

I live in a very tiny space, and recently bought a portable washing machine because the laundry in my building is very expensive and always seems to be in use.

The machine I bought works well, but there is no spin dry-- I wring out every piece of clothing and hang it in my bathroom (no patio or yard). It's been a day and everything is still damp and wrinkly, so I've been reluctant to wash my towels and sheets. Is there a better method for manual washing? I'm willing to buy a drying device, given it is small and works well enough. I need tips from other people who do their laundry this way!