The detailed anisotropic dispersion of the low-temperature, low-energy magnetic excitations of the candidate spin-triplet superconductor UTe2 is revealed using inelastic neutron scattering. The magnetic excitations emerge from the Brillouin zone boundary at the high symmetry Y and T points and disperse along the crystallographic b̂-axis. In applied magnetic fields to at least μ0H = 11 T along the ĉ−axis, the magnetism is found to be field-independent in the (hk0) plane. The scattering intensity is consistent with that expected from U3+/U4+ f-electron spins with preferential orientation along the crystallographic â-axis, and a fluctuating magnetic moment of μeff=1.7(5) μB. We propose interband spin excitons arising from f-electron hybridization as a possible origin of the magnetic excitations in UTe2.