Actually, the bags that we use don't have any padding, and there's only a pocket for the front wheel. This helps to make it not too large when folded down to carry in a pannier when riding. I wouldn't recommend this kind of bag for anything other than train travel or for putting a bike inside a car and keeping the vehicle's interior clean. For any other kind of bike transport, get a more serious bag or box, but for train travel then this is ideal.

I'm glad that people seem interested in this post; as a quick follow-up, another bike-transport tip is that you can take 2 bikes on a plane while only paying one surcharge by taking one box that contains two bikes. When we moved here from Canada with FOUR bikes (one road, one mountain bike each), we got two boxes custom-made at a local box factory, double-walled corrugated cardboard, each large enough for two bikes, each costing just 35 CHF. Of course, the bikes need to be packed and padded well, and it's best if you detach the handlebars as well as the normal front wheel and pedals to make the box as small as possible. We've kept the boxes and will use them again when we move next.

Happy riding!