We study in detail the scalar-field Hawking radiation emitted into the bulk by a higher-dimensional, rotating black hole. We numerically compute the angular eigenvalues, and solve the radial equation of motion in order to find transmission factors. The latter are found to be enhanced by the angular momentum of the black hole, and to exhibit the well-known effect of superradiance. The corresponding power spectra for scalar fields show an enhancement with the number of dimensions, as in the non-rotating case. On the other hand, the proportion of the total (i.e., bulk+brane) power that is emitted into the bulk decreases monotonically with the angular momentum. We compute the total mass loss rate of the black hole for a variety of black-hole angular momenta and bulk dimensions, and find that, in all cases, the bulk emission remains significantly smaller than the brane emission. The angular-momentum loss rate is also computed and found to have a smaller value in the bulk than on the brane
