You might think it impossible to wash anything with air but you would
I have not washed clothes with the pump. I did do a few trials washing the fine clay off fodder beet (for feeding sheep and cattle). Sheep love the big roots but they do not enjoy eating the clay that sticks to them.
You may need to make a few modifications to wash clothes.
Your pulser pump need only be 3 to 4 feet deep. This is to match the depth of your washing "machine" which is unlikely to be more than 30 inches deep. Shallow pumps produce a lot more air and it is air that you want to bubble up and churn the water.
If you have a big deep pulser pump that is powerful enough, do not despair. It can do 2 jobs at once!
As you can see from the diagram it is really simple to set up.
Rinsing and drying the clothes can be achieved with the following
set up. In this case, you need the higher pressure of the normal
pulser pump to blow air through. The water traveling through the clothes
(The bottom of the pipe is open to let the water out)
Below is an add-on to store pressure. The idea here is to open the valve quickly and release the air. It rushes through the packed together clothes forcing the water out! Easy, simple and effective.