Thanks everyone for the tips! I think with the complicated travel route and the short stays I'll probably be best off renting bikes in each city ... its expensive but wrorthwhile considering the hassle of transporting my own bike. Plus I'd hate to have my own stolen...
I think the deal breaker is that there are no direct flights to Passau. If there was one, I'd fly my bike there, travel to Vienna and then ship it back to the US at the end of my stay there. I'd rent a bike in Amsterdam ... but renting in all the cities seems to be the best option at this point - I can still travel with luggage and rent a bike with a saddlebag for day trips.