ABRIDGED: We use HSTACS and NICMOS imaging to study the structure and colors of a sample of nine late-type spirals. We find: (1) A correlation between bulge and disks scale-lengths, and a correlation between the colors of the bulges and those of the inner disks. Our data show a trend for bulges to be more metal-enriched than their surrounding disks, but otherwise no simple age-metallicity connection between these systems; (2) A large range in bulge stellar population properties, and, in particular, in stellar ages. Specifically, in about a half of the late-type bulges in our sample the bulk of the stellar mass was produced recently. Thus, in a substantial fraction of the z=0 disk-dominated bulged galaxies, bulge formation occurs after the formation/accretion of the disk; (3) In about a half of the late-type bulges in our sample, however, the bulk of the stellar mass was produced at early epochs; (4) Even these old late-type bulges host a significant fraction of stellar mass in a young(er) c component; (5) A correlation for bulges between stellar age and stellar mass, in the sense that more massive late-type bulges are older than less massive late-type bulges. Since the overall galaxy luminosity (mass) also correlates with the bulge luminosity (mass), it appears that the galaxy mass regulates not only what fraction of itself ends up in the bulge component, but also when bulge formation takes place. We show that dynamical friction of massive clumps in gas-rich disks is a plausible disk-driven mode for the formation of old late-type bulges. If disk evolutionary processes are responsible for the formation of the entire family of late-type bulges, CDM simulations need to produce a similar number of initially bulgeless disks in addition to the disk galaxies that are observed to be bulgeless at z=0.
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