Quarter-wave operation or a phase shift of more than $\pi/2$ , which is approximately ten times greater than that reported in previous works using liquid crystals (LCs) and graphene electrodes, was demonstrated. The device is transparent to the terahertz (THz) wave, and the driving voltage required was as low as approximately 2.2 V (rms), which is also unprecedented. Experimental results supported a theoretical formalism adapted for LC cells with THz wavelength-scale thickness. The scattering rate, DC mobility, and carrier mean free path of bilayer graphene were also determined using THz spectroscopic techniques; the parameters were inferior to those of monolayer graphene. This observation can be attributed to the higher density of charged impurities in the bilayer graphene. The device performances of LC phase shifters using monolayer and bilayer graphene as electrodes were essentially identical.