I do not have running water in my darkroom and I can work just fine. My darkroom is in the basement, right across the way from the laundry room where there is a large slop sink. I do all my print washing and film developing in the laundry sink.

For INSIDE the darkroom, I have two five gallon plastic buckets.
The first bucket contains clean water. I fill it up about 2/3 with water from the laundry sink. The second bucket is for slop.
When the clean bucket gets empty or when the slop bucket gets too full (usually pretty close to the same time) I take them out dump them down the drain, rinse them and fill up the clean bucket again.
I bought them at Home Depot just for the darkroom. I use them for nothing else.

It is, however, a big PITA to have to lug those dumb buckets back and forth all the time!