TL; DR: You can, maybe, in some places, but it may not be a good idea.
Whether it is legal, it depends on the Bundesland (state) – to put it simply, the federal government has no authority over this, and each state sets its own rules. There are federal rules for entering Germany, but these do not apply since you are already in the country.
Examples of rules
For example: in Saarland, they have set up a lock (perhaps because of their proximity to the most affected regions of France): you can only leave your home for "important reasons". On the other hand, Rheinland-Pfalz has a "contact ban", which means that you can freely go wherever you want, as long as you are not accompanied by another person.
In addition, individual cities have the right to be more restrictive.
The number of cases will increase in Germany and regulations could become tighter at any time. In this case, it may be difficult for you to return home (also: do not count on lifting the restrictions well after Easter – at best)
Infrastructure is stopped
However, even in Rheiland-Pfalz, accommodation is not open for tourist purposes. This will include campsites. Wilderness camping is only regulated by the Länder, but generally there will be restrictions and the camping pitches can be demarcated.
In addition, most public services useful to travelers are also closed.
It is difficult to say how things will be applied. Generally, there are no formal requirements in Germany, unlike Italy or France. They will always stop and fine you if you openly flout the rules. I guess no one is going to check out wilderness camping in the middle of nowhere, but they can check out popular campsites to make sure people don't congregate there.
Biking alone is not really an (additional) risk, as long as you don't meet people. However, the question is whether it will be a fun trip if you:
- I can't go to places like Saarland
- Stay alone all the weather
- You have to find a remote place to pitch your tent every night and you don't have access to the sanitary facilities
- You must bring / buy and cook your own food (there will be no restaurants)
In addition, Germany is a densely populated country – it will be difficult to really be alone. And as soon as more than one person sets up their tent in the same place, the police will probably see it as a "congregation" and separate it.
In all honesty, it's probably best to stay in one place. If local laws allow, you can still bike and go home each evening.