I had already a small folding bicycle with me ... in the train you can put it in a back and that's it !! Smile
I have a bike from this company: Dahon
It was about 300 EUR ... expensive but good quality ...
but I also meet already travellers using just a normal old bike, without light and all the stuff ... they just putted off the weehls before entering the train and then did the bike under the seat and covered it with a cover.