  We study a sample of 28 S0 galaxies extracted from the integral-field
spectroscopic (IFS) survey CALIFA. We combine an accurate two-dimensional (2D)
multi-component photometric decomposition with the IFS kinematic properties of
their bulges to understand their formation scenario. Our final sample is
representative of S0s with high stellar masses ($M_{star}/M_{sun} > 10^{10}$).
They lay mainly on the red sequence and live in relatively isolated
environments similar to that of the field and loose groups. We use our 2D
photometric decomposition to define the size and photometric properties of the
bulges, as well as their location within the galaxies. We perform mock
spectroscopic simulations mimicking our observed galaxies to quantify the
impact of the underlying disc on our bulge kinematic measurements ($\lambda$
and $v/\sigma$). We compare our bulge corrected kinematic measurements with the
results from Schwarzschild dynamical modelling. The good agreement confirms the
robustness of our results and allows us to use bulge reprojected values of
$\lambda$ and $v/\sigma$. We find that the photometric ($n$ and $B/T$) and
kinematic ($v/\sigma$ and $\lambda$) properties of our field S0 bulges are not
correlated. We demonstrate that this morpho-kinematic decoupling is intrinsic
to the bulges and it is not due to projection effects. We conclude that
photometric diagnostics to separate different types of bulges (disc-like vs
classical) might not be useful for S0 galaxies. The morpho-kinematics
properties of S0 bulges derived in this paper suggest that they are mainly
formed by dissipation processes happening at high redshift, but dedicated
high-resolution simulations are necessary to better identify their origin.
