We present a study of the X-ray spectral properties of the highly variable X-ray emitting black hole in a globular cluster in the elliptical galaxy NGC 4472. The XMM-Newton spectrum of the source in its bright epoch is well described by a multiple blackbody model with a characteristic temperature $kT_{in}approx$ 0.2 keV. The spectrum of an archival Chandra observation of the source obtained 3.5 years before the XMM data gives similar estimates for the blackbody parameters. We confirm that the fainter interval of the XMM-Newton observation has a spectrum that is consistent with the brighter epoch, except for an additional level of foreground absorption. We also consider other possible mechanisms for the variability. Based on the timescale of the X-ray flux decline and the estimated size of the X-ray emission region we argue that an eclipsing companion is highly unlikely. We find the most likely means of producing the absorption changes on the observed timescale is through partial obscuration by a precessing warped accretion disk.