We present 75As nuclear magnetic resonance spin-lattice and spin-spin relaxation rate data in Ba(Fe1−xCox)2As2 and Ba(Fe1−xCux)2As2 as a function of temperature, doping, and magnetic field. The relaxation curves exhibit a broad distribution of relaxation rates, consistent with inhomogeneous glassy behavior up to 100 K. The doping and temperature response of the width of the dynamical heterogeneity is similar to that of the nematic susceptibility measured by elastoresistance measurements. We argue that quenched random fields which couple to the nematic order give rise to a nematic glass that is reflected in the spin dynamics.