> The Germans don't really have any more right to it than she does.
Article 56 of the Hague Convention of 1907 disagrees. Stealing art is a war crime. So do the Allies themselves, in their memorandum on January 5th, 1943.
> The most likely story of this bust is from the 5th century until the 18th or 19th centuries, it was buried in the ground somewhere in Italy or former Roman empire.
Given that the person depicted was originally associated with Drusus Germanicus (the name's a hint here) and Aschaffenburg was in fact part of the Roman Empire back in the day, chances are they found it in the vicinity. The object is a lot more related to Aschaffenburg than Texas, which in fact never was part of the Roman Empire.
> But is that museum inherently this German one?
The wartime looting of art and/or cultural objects is barbaric as it robs the object of its historical context and the regions of their heritage. This is true regardless of the uniform that the criminal wore. If you think Germans should hand back art stolen before or during WW2, you cannot really argue against restitution demands for art stolen by Americans.