We measure the redshift evolution of galaxy bias for a magnitude-limited galaxy sample by combining the galaxy density maps and weak lensing shear maps for a ~116 deg2 area of the Dark Energy Survey (DES) Science Verification (SV) data. This method was first developed in Amara et al. and later re-examined in a companion paper with rigorous simulation tests and analytical treatment of tomographic measurements. In this work we apply this method to the DES SV data and measure the galaxy bias for a i <22.5 galaxy sample. We find the galaxy bias and 1σ error bars in four photometric redshift bins to be 1.12 ± 0.19 (z = 0.2-0.4), 0.97 ± 0.15 (z = 0.4-0.6), 1.38 ± 0.39 (z = 0.6-0.8), and 1.45 ± 0.56 (z = 0.8-1.0). These measurements are consistent at the 2σ level with measurements on the same data set using galaxy clustering and cross-correlation of galaxies with cosmic microwave background lensing, with most of the redshift bins consistent within the 1σ error bars. In addition, our method provides the only σ8 independent constraint among the three. We forward model the main observational effects using mock galaxy catalogues by including shape noise, photo-z errors, and masking effects. We show that our bias measurement from the data is consistent with that expected from simulations. With the forthcoming full DES data set, we expect this method to provide additional constraints on the galaxy bias measurement from more traditional methods. Furthermore, in the process of our measurement, we build up a 3D mass map that allows further exploration of the dark matter distribution and its relation to galaxy evolution.