Within the US I’d probably ship the bicycle. For a short tour in Europe I’d be tempted to rent a bicycle. The cost of the rental won’t be any more than the airline charges, and it’s a lot less of a hassle at either end. Bike by plane has become more of a PITA every time.
Most airlines will let you count your bicycle as one of your pieces of (non-carry-on obviously!) luggage when flying internationally. Often bicycles are free on European airlines, but most US airlines charge an additional fee of $200-$300 each way. Take note that the rates are often different when comparing domestic and international travel. Be warned – the travel agent, the people on the phone for the airline, and the people at the counter at the airport, won’t always agree on the airline policy. Not helping the situation, the people at the counter are often shared by different airlines, and won’t always know the policies for bicycles for that specific airline. When they disagree with you on cost at check-in, you’re unlikely to be able to argue the issue at the time, even if you’re carrying a print-out of their policies. Be prepared to pay up front and deal with it at the end of your trip. Another thing to check is the size of your airplane. If you’re flying on a smaller plane they can’t/won’t always fit the bike. The bike will end up on a later flight, but that’s a real pain. You also won’t always be told that was the plan, so when you arrive you will have to puzzle out where the bicycle went.
To ship the bike on the plane, you’ll want to protect it in some way. The requirements can vary by airline. Some will permit a cloth carrying case, but most will require a hard case. You can purchase an actual bicycle carrying case. These are expensive, and you have to figure out what you’re going to do with it once you’re off the plane, because you’re unlikely to want to throw that much money away. I’ve instead always used a cardboard bicycle box. Unlike a hard case, you can treat the box as disposable. When I’m cycling in a circle I’ve left the box at the hotel/hostel where I started, but since recently I’ve been traveling in a line (“open jaw”) I’ve abandoned the box upon arrival and gone to a local bike shop in my departure city to get another one. Given yourself a day or two at the end of the trip to work that out.
You used to be able to buy boxes from the airline for $10-$15. Those boxes were great, big enough that you can just remove the pedals and turn the handlebars sideways. Unfortunately, few airlines still offer this. You should be able to pick up a box at your local bicycle store. Unfortunately, the boxes from a bike shop from new bikes are typically smaller than those from the airline, so be prepared to have to remove the fenders and front rack in addition to the usual handlebars and pedals. In the most extreme of cases, you could also have to remove the front fork. The bicycle boxes from REI are nice/bigger. Their boxes used to be free until someone realized they could make a profit; it’s about $10 now.
The problem when I use cardboard boxes is the cardboard handholds on the box are not strong enough. When the luggage handlers pick up the box, they rip out the handles, and after that are forced to (as best I can tell) throw the box around to move it. To address this I cut 1/4″ plywood, and glue it on the inside of the handles for reinforcement (with a hole cut to match the box in the piece of 12″ x 4″ plywood). This makes the handles strong enough the box can be moved by the handles, making the box easy to pick up, and the whole assembly tends to travel much better.
When packing the bicycle, you can also pack much of your gear into the box with the bicycle (paying attention to weight limits, somewhere between 50-70 lbs.). I usually have all of the lighter items packed in with the bicycle. You also should deflate the tires even though the cargo space is pressurized, if only because some airlines will insist. I’ve even had to unpack my bicycle just to prove that I’d deflated the tires. I also worry about something heavy being placed on top of the forks, so I also reinforce the front forks with a threaded bolt and some washers.
One thing that can make a bike easier to transport is S&S couplers. They’re expensive but effectively let you snap the bike in half. There are places that will consider doing it after you purchase the bicycle, but the best option is having them installed by the manufacturer at the time the bicycle frame is purchased.
Some countries move bicycles (and people) primarily by bus. Ireland, for example, is almost 100% bus-oriented, and significantly cheaper than train. And Ireland is small enough that buses are frequently as fast as trains. If the buses move bicycles, the bicycle will typically go in the space in the undercarriage. If there’s not room, you will end up waiting for the next bus.
The European train systems are all generally familiar with the concept of transporting bicycles. However, how familiar, and what the process is, varies WILDLY by country.
Some day I’ll get around to including pictures of various road signs.