How can the radius of a bare neutron be negative?

If you compare with another source, like the neutron data from the Particle Data Group, you'll find that what is called R in your source is what the PDG booklet calls "mean square charge radius" (see p. 5 in the PDF).

Now the negative sign for the charge radius is just a convention you use when dealing with the neutron, which is an uncharged particle. The corresponding Wikipedia article states:

In [the case of a particle with net zero electric charge], the square of the charge radius of the particle is defined to be negative, with the same absolute value with units of length squared equal to the positive squared charge radius that it would have had if it was identical in all other respects but each quark in the particle had the opposite electric charge (...)

The best known particle with a negative squared charge radius is the neutron. (...)

The table refers to the electric charge radius which can be both negative or positive, depending on the distribution of charge. The reason we focus on the charge radius rather than (for example) the baryon radius is because the electric charge radius can be measured in electron scattering, whereas the Baryon charge radius cannot be directly measured.

The fact that the neutron charge radius is negative means that we can picture the neutron as a positively charged core surrounded by a negatively charged corona. A simple explanation of this fact is provided by the idea that Quantum mechanically the neutron sometimes fluctuates into a proton and a negatively charged pion. The proton is heavy and forms a positively charged core, where is the pion his light and forms a cloud. Note that the neutron can also fluctuate into a negatively charged Delta resonance and a positively charged pion, but this process is less likely because the Delta resonance is heavy.