I would use a plastic tote box of the appropriate size to carry it and tools I need (in their own small plastic box) to carry these various places to sew and work on them. You can more easily manipulate the portion you are working on and yet keep the bulk of it controlled and clean within the confines of the tote box. It is no harder to carry than a cloth or plastic bag. Like the others have said, shun the garbage bag. I know someone who had a wonderful quilt in progress get pitched in the trash because several 'volunteer helpers' came to help break down a quilt show.