  We present evidence for nuclear spin-lattice relaxation driven by glassy
nematic fluctuations in isovalent P-doped BaFe$_2$As$_2$ single crystals. Both
the $^{75}$As and $^{31}$P sites exhibit stretched-exponential relaxation
similar to the electron-doped systems. By comparing the hyperfine fields and
the relaxation rates at these sites we find that the As relaxation cannot be
explained solely in terms of magnetic spin fluctuations. We demonstrate that
nematic fluctuations couple to the As nuclear quadrupolar moment and can
explain the excess relaxation. These results suggest that glassy nematic
dynamics are a universal phenomenon in the iron-based superconductors.
