A theoretical study of the rotational dynamics of H, molecules trapped in the interstitial channels of a carbon nanotube bundle is presented. The potential used in this study is modeled as a sum of atom-atom (C-H) van der Waals interactions and electrostatic interactions of the molecule with the surrounding nanotubes. The rotational energy spectra is calculated using a product wave function, where the coupling between translational and rotational modes is treated in a mean-field manner. A molecular dynamics simulation study was performed for estimating the hydrogen rotational barrier. Both theoretical calculations and simulation results reveal the existence of a large rotational barrier (similar to40 meV). The consequences of this rotational barrier for the rotational energy levels are worked out in detail.