We measure optical colors for the bulges of 312 disk galaxies from the Carnegie-Irvine Galaxy Survey and convert their previously available R-band structural parameters to stellar-mass parameters. We also measure their average stellar-mass surface density in the central 1kpc ({Sigma}1). Comparing the mass-based Kormendy relation with the original one based on flux, we find that the majority of the classifications into classical and pseudo bulges, as well as their overall statistical properties, remain essentially unchanged. While the bulge-type classifications of the Kormendy relation are robust against stellar population effects, the mass-based classification criteria do produce better agreement between bulge structural properties and their stellar populations. Moreover, the mass-based Kormendy relation reveals a population of ultradense bulges akin to high-z compact early-type galaxies, which are otherwise hidden in the original Kormendy relation. These bulges are probably relics of spheroids assembled in the early universe, although for some we cannot rule out some contribution from secular growth. We confirm previous studies that {Sigma}1 correlates well with bulge surface densities.