The style is not entirely unique in portraiture, but it is quite rare for Roman emperors.

The bust does represent Nero, but it is inauthentic in another way: it is mostly a restoration. If you zoom in on the face (for instance in this picture of the bust) you will see that the forehead and parts of the hair and nose are in a different colour; these are the only surviving ancient parts of the sculpture, the rest being created during the Renaissance. However the reconstruction is not that different from how he looks in genuine busts and coins (see here and here, for example).

I am not aware of any earlier example of this beard-style in Roman art, but we do have several from the Hellenistic kings, notably the Ptolemies and Seleucids (here and here are members of the former, and this, this and this being of the latter dynasty). It could be that Nero adopted the style due to its associations with Hellenistic kings, since he was very interested in Greek culture (even taking part in the Olympics!) and seems to have attempted a more Hellenistic style of rulership. Though I have also seen the argument that it was a military style.

Later the emperor Titus is also shown with a neckbeard on some coins (like these). And during the Flavian period we have some other busts portraying men with similar styles: for example this in the Met Museum and this one (previously misidentified as Josephus*) in the Glyptotek in Copenhagen. Note that both of these also have slight moustaches so they are not precisely the same style, but quite similar. Far later the emperors Decius and Tacitus are also depicted with a sort of neckbeard, though this was at a time when short-cropped beards or stubbles were in fashion rather than the shaven faces of the pre-Hadrianic Imperial period.

The question of Nero's beard was also discussed some time ago by u/Deirdre_Rose, if you are interested in a different perspective on it.

* I found an chapter about this bust and its rather racist misidentification published this very year: "Testa incognita: The History of the Pseudo-Josephus Bust in Copenhagen" in Ancient Jewish Diaspora: Essays on Hellenism by René Bloch, which was useful and very interesting.