A microlensing survey by Sumi et al. (2011) exhibits an overabundance of short-timescale events (t E 2 days) relative to that expected from known stellar populations and a smooth power-law extrapolation down to the brown dwarf regime. This excess has been interpreted as a population of approximately Jupiter-mass objects that outnumber main-sequence stars by nearly twofold; however the microlensing data alone cannot distinguish between events due to wide-separation (a 10 AU) and free-floating planets. Assuming these short-timescale events are indeed due to planetary-mass objects, we aim to constrain the fraction of these events that can be explained by bound but wideseparation planets. We fit the observed timescale distribution with a lens mass function comprised of brown dwarfs, main-sequence stars, white dwarfs, neutron stars, and black holes, finding and thus corroborating the initial identification of an excess of short-timescale events. Including a population of bound planets with distributions of masses and separations that are consistent with the results from representative microlensing, radial velocity, and direct imaging surveys, we then determine what fraction of these bound planets are expected not to show signatures of the primary lens (host) star in their microlensing light curves, and thus what fraction of the short-timescale event excess can be explained by bound planets alone. We find that, given our model for the distribution of planet parameters, bound planets alone cannot explain the entire excess without violating the constraints from the surveys we consider, and thus some fraction of these events must be due to free-floating planets, if our model for bound planets holds. We estimate a median fraction of short-timescale events due to free-floating planets to be f = 0.67 (0.23-0.85 at 95% confidence) when assuming "hot-start" planet evolutionary models and f = 0.58 (0.14-0.83 at 95% confidence) for "cold-start" models. Assuming a delta-function distribution of free-floating planets of mass m p = 2 M Jup yields a number of free-floating planets per main sequence star of N = 1.4 (0.48-1.8 at 95% confidence) in the "hot-start" case and N = 1.2 (0.29-1.8 at 95% confidence) in the "cold-start" case.