We demonstrate efficient linear-optical access to surface-state spin dynamics in Bi2Se3 by probing transitions between two surface-state Dirac cones, providing a practical technique for spin-current dynamics studies in topological-insulator devices. Using broadband transient-reflectivity pump-probe measurements, we distinguish bulk and surface state-responses, by controlling photon energy and circular polarization at oblique incidence. For pump-photon energies corresponding to bulk-state transitions, the probe polarized co-circularly with the pump shows stronger reflectivity change, compared to the anti-circularly polarized probe. However, pump photon energies corresponding to surface-state transitions result in an opposite effect, with the anti-circularly polarized probe exhibiting stronger reflectivity change. This surprising behavior stems from the surface-state in-plane spin orientation near the Dirac point, and the surface-state spin population remains at the injected energy for several ps. These results enable an efficient approach for studying spin current dynamics in topological-insulator based technologies.