We present ground-based and HST optical and infrared observations of Swift XRF 100316D / SN 2010bh . It is seen that the optical light curves of SN 2010bh evolve at a faster rate than the archetype GRB-SN 1998bw , but at a similar rate to SN 2006aj , a supernova that was spectroscopically linked with XRF 060218 , and at a similar rate to non-GRB associated type Ic SN 1994I . We estimate the rest-frame extinction of this event from our optical data to be E ( B - V ) = 0.18 \pm 0.08 mag . We find the V -band absolute magnitude of SN 2010bh to be M _ { V } = -18.62 \pm 0.08 , which is the faintest peak V -band magnitude observed to-date for a spectroscopically-confirmed GRB-SNe . When we investigate the origin of the flux at { t - t _ { o } = 0.598 } days , it is shown that the light is not synchrotron in origin , but is likely coming from the supernova shock break-out . We then use our optical and infrared data to create a quasi-bolometric light curve of SN 2010bh which we model with a simple analytical formula . The results of our modeling imply that SN 2010bh synthesized a nickel mass of { M _ { Ni } \approx 0.1 M _ { \odot } } , ejected { M _ { ej } \approx 2.2 M _ { \odot } } and has an explosion energy of { E _ { k } \approx 1.4 \times 10 ^ { 52 } } erg . Thus , while SN 2010bh is an energetic explosion , the amount of nickel created during the explosion is much less than that of SN 1998bw , and only marginally more than SN 1994I . Finally , for a sample 22 GRB-SNe we check for a correlation between the stretch factors and luminosity factors in the R band and conclude that no statistically-significant correlation exists .