You can force your shower towel to dry faster by using clothes pins to hang on the shower rod.
The more the surface area is exposed, the faster it will dry. When doubled over the rod the surface area is decreased.
You can purchase fast drying towels, actually any cheap Chinese nylon towel wil dry very fast, the problem is they do not dry your body well. I carry a large towel, I often have to walk to a share shower, so I need to cover my body.