  (Abridged) The structural parameters of a magnitude-limited sample of 148
unbarred S0-Sb galaxies were analyzed to derive the intrinsic shape of their
bulges. We developed a new method to derive the intrinsic shape of bulges based
on the geometrical relationships between the apparent and intrinsic shapes of
bulges and disks. The equatorial ellipticity and intrinsic flattening of bulges
were obtained from the length of the apparent major and minor semi-axes of the
bulge, twist angle between the apparent major axis of the bulge and the galaxy
line of nodes, and galaxy inclination. We found that the intrinsic shape is
well constrained for a subsample of 115 bulges with favorable viewing angles. A
large fraction of them is characterized by an elliptical section (B/A<0.9).
This fraction is 33%, 55%, and 43% if using their maximum, mean, or median
equatorial ellipticity, respectively. Most are flattened along their polar axis
(C<(A+B)/2). The distribution of triaxiality is strongly bimodal. This
bimodality is driven by bulges with Sersic index n>2, or equivalently, by the
bulges of galaxies with a bulge-to-total ratio B/T>0.3. In particular, bulges
with n\leq2 and with B/T\leq0.3 show a larger fraction of oblate axisymmetric
(or nearly axisymmetric) bulges, a smaller fraction of triaxial bulges, and
fewer prolate axisymmetric (or nearly axisymmetric) bulges with respect to
bulges with n>2 and with B/T>0.3, respectively. According to predictions of the
numerical simulations of bulge formation, bulges with n\leq2, which show a high
fraction of oblate axisymmetric (or nearly axisymmetric) shapes and have
B/T\leq0.3, could be the result of dissipational minor mergers. Both major
dissipational and dissipationless mergers seem to be required to explain the
variety of shapes found for bulges with n>2 and B/T>0.3.
