My washer has an express cycle. I use little soap, but if I have some lightly soiled regular laundry, I throw that in too. I wash in warm and just do the default dryer setting. If you pay attention and take the fabric out as soon as it's dry, very little ironing is needed.
I know people say that the quilting will stabilize fabric that's not been pre shrunk, I'm still very uncomfortable with that. Do an experiment. Take a piece of quilting cotton. Measure both its length and width. Wash & dry. Now re-measure. You will probably find that it has shrunk an inch or two selvedge to selvedge.
Batiks will not shrink, but they sure can bleed!