We have utilized time-domain magnetoterahertz spectroscopy to investigate the low-frequency optical response of the topological insulator Cu_{0.02}Bi_{2}Se_{3} and Bi_{2}Se_{3} films. With both field and frequency dependence, such experiments give sufficient information to measure the mobility and carrier density of multiple conduction channels simultaneously. We observe sharp cyclotron resonances (CRs) in both materials. The small amount of Cu incorporated into the Cu_{0.02}Bi_{2}Se_{3} induces a true bulk insulator with only a single type of conduction with a total sheet carrier density of ~4.9×10^{12}/cm^{2} and mobility as high as 4000 cm^{2}/V·s. This is consistent with conduction from two virtually identical topological surface states (TSSs) on the top and bottom of the film with a chemical potential ~145 meV above the Dirac point and in the bulk gap. The CR broadens at high fields, an effect that we attribute to an electron-phonon interaction. This assignment is supported by an extended Drude model analysis of the zero-field Drude conductance. In contrast, in normal Bi_{2}Se_{3} films, two conduction channels were observed, and we developed a self-consistent analysis method to distinguish the dominant TSSs and coexisting trivial bulk or two-dimensional electron gas states. Our high-resolution Faraday rotation spectroscopy on Cu_{0.02}Bi_{2}Se_{3} paves the way for the observation of quantized Faraday rotation under experimentally achievable conditions to push the chemical potential in the lowest Landau level.