  The global colors 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. Therefore thee 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 $B/T$. 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. (3) 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 ... (Abridged)
