Linking trip between Valencia & Milan

We are flying from Australia to Madrid and riding to near Valencia in Spain for a 6 week period. Then we want to spend a few more weeks in the Italian Alps in the Arabba Dobbiaco. We will ride from Dobbiaco to Munich and home to Australia. We would like to get a train from Valencia to Milan. We are happy to spend a few days off the train somewhere like Lyon in France. But our trouble at the moment is travelling with our bikes on trains on this journey without having to pack them into a box at each part of the trip. We cannot take bike travel cases with us because we will be doing week long legs on the trip. Suggestions from people who travel in southern europe would be much appreciated. We are limited by our 90 days Schengen limit in EU.