Another way to wash small pieces or pre-cuts is with a salad spinner. Soak the fabric pieces in hot water (in the sink) with a bit of soap. Smoosh them a bit to "agitate" drain, rinse thoroughly. then put in the salad spinner and spin out the excess water. Smooth out and by the time you get them all spun you can press them dry. Keeps from fraying and is fast.
Pati, in Phx