I've traveled with two "suitcaseable" bikes: an S&S coupled one and a Bike Friday NWT. The S&S bike is, by far, much harder to get into its hard-sided case and maneuver around. The Bike Friday lives in the UK and came with (purchased separately) hard-sided Samsonite case for travel.
Packing the S&S bike takes me about 90 minutes when all the disassembly is added in. At first, I used the padding that came with the bike. But, it added enough weight to push the entire case over the magic 50 pounds. So, I switched to wrapping the bike in old tubes sliced up and zip-tied to the bike's frame parts. This saved weight and, frankly, protected the frame better. I tried a number of ways to make it easier for the TSA goons to search this case, which is opened most every time I fly with it. I tried zip-tying the entire assembly together, but TSA always just cuts the zip-ties. I've tried putting notes in the box with photos. They seemingly were ignored. I've flown with this bike dozens of times and not once has anything been broken or has the case not arrived with me. That said, the frame's paint is so dinged up that I no longer care what it looks like.
These days, my preferred destinations are in Europe. Since the Bike Friday lives in the UK, I don't have to fly from the US with a bicycle. Packing up the Bike Friday takes about 15-20 minutes as the entire bike frame, minus the wheels and the handlebars, when folded fits into the suitcase. This bike also came with padding, but I already know it will get dinged up so I don't bother using it as it adds a fair about of both time and bother to the process. Instead, I just insert padding between the metal parts. One downside of the BIke Friday case is that it is bigger than 62 linear inches by a bit. But, the international rules are different than the ones used in the US. Also, I've never had anyone measure it. So far, the case, which scraped up, has held up and always arrived on time.
For my recently canceled trip, I had planned to take some trains. I bought a bag designed for the Bike Friday that handles the folded bike and a bag or two. I planned to put the bike in the bag and carry it onto the train, saving the hassle of either getting a special ticket for the train or being told I can't take the bike on the train. I'll have to wait to see if this works, if I ever get the chance to tour by bike again!
A couple things:
I fully agree with the above suggestion to take step-by-step photos of how you put the bike in the box and take these with you. Without these, I'd have to reinvent my packing method on the S&S bike each time and it isn't all that easy to do even with the instructions.
Get some touch-up paint or nail polish to cover the dings the bike is going to get when it travels.
When I don't ride a loop route, I simply send my hard-sided case to my destination. This usually costs from $70 - $100 from a private shipper (UPS, FedEx, etc). In the Netherlands, the postal service sent it to Germany for about $25.