The global colors and structure of galaxies have recently been shown to follow bimodal distributions. Galaxies separate into a “red sequence”, populated prototypically by early-type galaxies, and a “blue cloud”, whose typical objects are late-type disk galaxies. Intermediate-type (Sa-Sbc) galaxies populate both regions. It has been suggested that this bimodality reflects the two-component nature of disk-bulge galaxies. However, it has now been established that there are two types of bulges: “classical bulges” that are dynamically hot systems resembling (little) ellipticals, and “pseudobulges”, dynamically cold, flattened, disk-like structures that could not have formed via violent relaxation. Alas, given the different formation mechanisms of these bulges, the question is whether at types Sa-Sbc, where both bulge types are found, the red-blue dichotomy separates galaxies at some value of disk-to-bulge ratio, B/T, or, whether it separates galaxies of different bulge type, irrespective of their B/T. In this paper, we identify classical bulges and pseudobulges morphologically with HST images in a sample of nearby galaxies. Detailed surface photometry reveals that: (1) The red blue dichotomy is a function of bulge type: at the same B/T, pseudobulges are in globally blue galaxies and classical bulges are in globally red galaxies. (2) Bulge type also predicts where the galaxy lies in other (bimodal) global structural parameters: global Sérsic index and central surface brightness. Hence, the red blue dichotomy is not due to decreasing bulge prominence alone, and the bulge type of a galaxy carries significance for the galaxy's evolutionary history.