You can wash jelly rolls, but test the method I am suggesting on scraps to see if you like the results.
Safety pin 5 jellyroll strips together, End. Middle, other end. Do this until all strips are pinned. Put them in a lingerie bag, zip it shut. Wash in cold or warm water on gentle. (Use color catchers if you want.)
When done, hang individual strips over towel racks/shower curtain until dry.
I rarely do this, though.