  Reverberation mapping (RM) has long been a powerful tool for measuring the
masses of supermassive black holes (SMBHs) at the centers of active galactic
nuclei (AGNs), but the precision of these mass measurements depends on the
so-called virial factors. It has been demonstrated that the virial factors
exhibit significant diversity, spanning approximately 1-2 orders of magnitude
across different AGNs. However, the underlying physical drivers for the
diversity have not yet been finalized. Here, adopting the SMBH mass -- spheroid
luminosity relations of inactive galaxies with different bulge classifications,
we calibrate the virial factors corresponding to the AGNs with pseudobulges
(PB) and classical bulges (or elliptical hosts, CB) using the latest nearby RM
sample. We investigate the correlations between virial factors and the AGN
spectral properties, and find that for both PB and CB samples, the FWHM-based
virial factors exhibit significant anti-correlations with the emission-line
widths and profiles, while the $\sigma_{\rm line}$-based virial factors only
show moderate anti-correlations with line widths for PB. We attribute these
correlations mainly to the inclination angle or opening angle of the broad-line
regions. Moreover, we establish new relations to give more precise virial
factors and, in combination with the latest iron-corrected radius-luminosity
relation, develop tentatively new single-epoch estimators of SMBH masses, which
enable more accurate measurements of SMBH masses in large AGN samples.
