The way I do it now is to get a used bike box from halfords for travelling out and a bike bag plastic or better for return. This is the way to do it. It's secure in a sturdy cardboard box.I bought a proper bike bag that was £40. Folded up and takes the whole top compartment of my panniers. Friends who I cycled with just used the clear plastic bag. Bought 2. Bin the one when you arrive and then your have a fresh new one for returning. No weight in them and take take up minimal space.
Bear in mind I always travel from point A to Point B and not circular.