We perform an analysis of two-point galaxy clustering and galaxy bias using Subaru Hyper-Suprime Cam (HSC) data taken jointly by the Subaru Strategic Program and the University of Hawaii in the COSMOS field. The depth of the data is similar to the ongoing Hawaii Two-0 (H20) optical galaxy survey, thus the results are indicative of future constraints from tenfold area... We measure the angular auto-power spectra of the galaxy overdensity in three redshift bins, defined by dropouts from the g-, r- and i-bands, and compare them to the theoretical expectation from concordance cosmology with linear galaxy bias. We determine the redshift distribution of each bin using a standard template-based photometric redshift method, coupled with a self-organizing map (SOM) to quantify colour space coverage. We also investigate sources of systematic errors to inform the methodology and requirements for Hawaii Two-0. The linear galaxy bias fit results are $b_{\mathrm{gal,g}} = 3.90 \pm 0.33 (\mathrm{stat}) \substack{ +0.64 \\ -0.24 } (\mathrm{sys})$ at redshift $z \simeq 3.7$, $b_{\mathrm{gal,r}} = 8.44 \pm 0.63 (\mathrm{stat}) \substack{ +1.42 \\ -0.72 } (\mathrm{sys})$ at $z \simeq 4.7$, and $b_{\mathrm{gal,i}} = 11.94 \pm 2.24 (\mathrm{stat}) \substack{ +1.82 \\ -1.27 } (\mathrm{sys})$ at $z \simeq 5.9$. (read more)