We have measured Mg_2_, Fe5270 and Fe5335 spectrophotometric indices (LICK system) in the bulge of 89 galaxies, mostly spirals from the Heraudeau sample. The indices are reduced to a null velocity dispersion and normalized to an aperture of 0.2h^-1^kpc. The mean errors are 0.009 mag on Mg_2_, and 0.3{AA} on the iron indices. These measurements almost double the amount of similar data already available on spiral galaxies. Our data confirm the existence of the relation between Mg_2_ and sigma_0_, the central stellar velocity dispersion; and we find an even tighter relation between Mg_2_ and Vmaxrot, the maximum rotational velocity of the galaxy, deduced from HI observations. For the most massive bulges these correlations may be interpreted as a mass-metallicity relation. However, the presence of young stellar populations, traced by the detection of [OIII]{lambda}500.7nm emission, provides a clear evidence that age effects play a role. Since the contribution of the young population is anti-correlated with the mass of the galaxy, it continues the Mg_2_ vs. sigma_0_ relation toward the low sigma_0_ and globally increases its slope. We present also evidence for a new positive correlation between Fe indices and sigma_0_ and for a significant correlation between the line strength indices and the total or disk luminosity. We propose to model the whole sequence of bulges within the following framework: Bulges are composed of a primary population formed prior to the disk during the initial collapse and a secondary population formed along the evolution. The whole family of bulges can be classified in three classes: (A) The bulges dominated by a young population are generally small, have ionized gas, low velocity dispersion and low line strengths. (B) The bulges dominated by the primary population lie along the mass metallicity sequence defined for elliptical galaxies. (C) The bulges where the secondary population is significant are less Mg-overabundant than B-type bulges and deviate from the Mg_2_ vs. sigma_0_ relation of elliptical galaxies. The original data are available in Hypercat: http://www-obs.univ-lyon1.fr/hypercat The tables of measurements and the extracted 1D spectra are also available in the present archive set.