Bismuth (Bi) has a double-layered structure based on Peierls distortion in crystalline phase. Complicated static structure in liquid phase which cannot be interpreted by a simple packing model has been conjectured that Peierls distortion may remain even in liquid phase. We measured quasi-elastic neutron scattering (QENS) of liquid Bi by using AMATERAS installed at BL14 beamport of Materials and Life Science Experimental Facility (MLF) in J-PARC and analyzed coherent QENS spectra. A time-space correlation function revealed that the nearest neighboring shell followed by a shoulder-like structure at longer side consists of four contributions of short and long correlations with relatively long relaxation time of a few tens pico second and medium-ranged and the longest correlations with a short relaxation time of sub-pico second, which is a direct observation of the existing layered structure in liquid Bi. In this article, we report the above scientific results and the method to analyze coherent QENS by the time-space correlation function.