Melk and Krems both sit on real rail lines
Neither end of the route requires a car.
From Vienna
Melk is on the main western railway corridor out of Vienna, with direct trains running under an hour and a half. Krems is reachable from Vienna on its own direct line in roughly an hour. Either end works as a day-trip base from Vienna, or as a start point if you're arriving from further afield and connecting through Vienna's main stations.
Along the valley itself
The Franz-Josefs-Bahn railway runs along the Wachau's north bank, stopping in most of the villages the cycle route passes through, including Krems. That's what makes a one-way ride genuinely practical here: start in Melk, finish in Krems (or the reverse), and take the train back to wherever your car, hotel, or onward journey is — no need to ride the same 36 km twice in one day.
Bringing a bike on the train
Regional Austrian trains along this corridor generally accommodate bikes, which matters if you've brought your own rather than renting locally — worth checking current bike-carriage rules and any reservation requirement for the specific train before you commit to a one-way plan, since these details change and aren't worth guessing at here.