Self guided biking-from Vienna along Danube river

My suggestion is to rent a bike from Nextbike. You can drop your bike at the end of your tour and need not to take it back by train.
Here are the Nextbike locations along the river Danube:
https://www.nextbike.at/niederoesterreich/en/locations/

Because within the Vienna city area there is a different bike renting system, Nextbike has only a few pick-up places in Vienna. Best for your trip would be Hütteldorf but it would require to bike about 10 miles across the city to reach the river Danube. You may take your bike and use the subway instead; outside peak hours it is permitted to use the subway with a bike, but not the trams or busses.

As an alternative you could go by train to Klosterneuburg, the first town outside Vienna in the north, and pick up your bike there, having the advantage to be at the river Danube already.

I am a huge fan of NextBike, but I would not recommend it for a longer journey as the bikes are very heavy and uncomfortable for longer distances.

In German, you want to google fahrradverleih (fahrrah = bike; verleih = rental). The Vienna tourist board's website has a few places recommended for bike rentals here - https://www.wien.info/de/lebenswertes-wien/sport/radfahren/fahrrad-verleih-345670#11/48.2075/16.3747. I'm sure they could also make sure you have helmets and any other gear you might need.

As for the route, you definitely want to do the Krems to Melk for one of your two days. I think it might be a bit far to go from Vienna to Krems in one day, but maybe you can find a good place to break things up because the overall distance from Vienna to Melk by bike is about 80 miles. Keep in mind that there is plenty to see in these areas, so allow time for that. It is then very easy to return to Vienna by train from Melk, but you will need a ticket for the bike.

I recommend a fun biking excursion in the city: the Ringstrasse. The Ringstrasse is a 3.5-mile-long circular route that encloses pre-modern era Vienna and mirrors the location of the old city wall, which is gone. Along the Ringstrasse, you will find at least 20 to 30 historical and cultural sites. If you acquire Rick's Vienna guide, he points out each of these sites via an easy-to-follow map and tells you what you're looking at, why it's important and so on. I rented a bike for a $5 from one of the bike-sharing services for eight hours or so, rode the entire route and saw these sites.

Postscript: Though Vienna's city wall is gone, there is a portion of an ancient Roman wall still standing on the Ringstrasse.

... there is a portion of an ancient Roman wall still standing on the Ringstrasse.

That part of the wall dates back to the late 17th and early 18th century.

I think Craig is thinking of a portion of the Roman military barracks which was unearthed in more recent times. It is located just in front of the main Hofburg entrance - free for all to see. But it isn’t on the Ring.

I know the Roman ruins by Hofburg Palace. I recall a different set of ruins visible from the Ringstrasse. I thought Rick said in his book that they were from Roman times, but maybe I misread his description or are misremembering them. Maybe wmt1 is right. My bad.

It would be a good idea to get a Bikeline book for the sections you're thinking about covering.