Hello & good luck
I just finished riding the
camino frances on my bike. Approx 500 miles.
Here's what I found.
Regardless of whether you have a folding bike or a regular size bike, the airlines will require that you have some type of suitable packing for the bike. In my case, our bike club has a hard shell bike case that also meets the european train standards (48" l x 36" h x 16" wide) It's expressed in centimeters and believe me they will check.
If you do not have a bike box or suitable bike bag, there are companies in the u.s. that will rent these to you for a short period of time (cost approx $250).
When you arrive at the airport, the airlines will charge you extra to ship the bike box/bag. If you tell them that the box contains a bike, they will charge you one tariff. If you tell them that the box contains 'sporting goods' they will charge you a lower tariff (go figure). That extra fee will get you from your home departure city to your destination city.
Now comes the interesting part. You are in your destination city and you have now assembled your bike. What do you do with the bike box? This means two problems to solve: one is where you store the bike box and the other is the fact that you have to come back to the same spot to pick up your bike box at some later point in your itinerary.
Usually, the hotel where you stay at your arrival city can arrange to accept your bike box for a nominal daily fee. You can also store the bike box at many of the airports or train stations (Consigna) but this is at a much higher daily fee rate.
Moving on: If, after arriving at your destination city, you have assembled the bike but then want to take a bus or a train to another city, you have to source a suitable bike carry bag. The bus stations (ALSA) sell these for about 10 euros and the folks at the train station will just give you a blank stare (get used to this).
I found the bus companies far easier to deal with as it relates to a bike packed in a bike bag. The bag fits down below in the cargo hold of the bike. For the trains in Spain, you have to wait for 20 min. before your departure before you can board and this means a mad scramble to get your bike in the train section that holds the larger luggage and then back to your seat. The folks at the train station like to get out their tape measures to confirm that your bike bag does not exceed size limits. You should plan to carry this bike bag with you during the duration of your ride on the camino (it folds up small size).
the trains in spain are sleek, modern, on-time and fast and a joy to ride. If I had it to do all over again, I would likely not use the trains at all, relying instead on bus for transportation.
I would very seriously consider renting a bike if you can complete your journey in a short period of time. the cost of the rental and convenience is less than the hassle of securing a bike box, blah, blah blah.
See my first statement for reassurance.
Buen camino!