I'd say the greener way is to reuse, at least for as long as possible. Buy a better quality roller brush that lasts longer. When I've been painting and needed to continue rolling the next day, instead of washing the roller, I put it in a plastic sack, tightly wind it around the roller to get rid of the air inside, twist tie it closed and put in the refrigerator until the next day.
If you're concerned about water consumption to clean the roller when you're done, try using "gray" water for the initial washing - that is, water saved from the shower (put a bucket in the shower) or the water from hand-washing dishes... Save that water in a container, then use it for your roller and brush clean-up after you're done. If you feel a final rinse in totally clean water is needed, then at least you cut down on the water used for painting clean-up.