I use plastic bins when transporting costumes, including a huge petticoat I have. it keeps things from getting crushed, while also keeping everything neat and easily accessible. Bags just make everything slide around, then items get further crushed or wrinkled while you're digging through trying to find something. Plus, you can use the bin as a little table later when laying out items or putting on makeup.
the plastic bins take up more room than a bag because they can't be smooshed into a corner. but that's the point: it keeps things from getting mangled and crammed when other people shove their luggage in with yours.