A theoretical investigation into the transport of fast ions from neutral beam injection in a Tokamak with a bundle divertor is presented. The principal loss mechanism introduced by the bundle divertor is the cross-field drift of particles trapped between the toroidal magnetic field mirror and the divertor ripple maxima. This mechanism causes a significant proportion of the usual banana-trapped region of velocity space to become a loss region. Analytic approximations for the velocity-space loss-region boundaries are derived. An analytic method is developed to estimate the resulting fast-ion energy loss and the energy transfer to the background-plasma ions and electrons. The fast-ion energy loss during neutral injection into DITE with the Mk II bundle divertor is predicted, using this method, to be no greater than 12% of the total injected energy. This compares favourably with the figure of 7% obtained by Monte-Carlo simulation.