  We use high-resolution numerical simulations to follow the barred disk
evolution in a suite of models with progressively more massive stellar bulges,
with bulge-to-total (disk$+$bulge) mass ratios of $B/T\sim 0-0.25$, embedded in
dark matter (DM) halos with the spin $\lambda \sim 0 - 0.09$. We focus on
models with a sequence of initial rotational support for bulges, and analyze
their spinup and spindown. We find that (1) the presence of a bulge affects the
evolution of stellar bars, i.e., the timescale of bar instability, bar pattern
speed and its decay, and the vertical buckling instability. The bar strength is
nearly independent of $B/T$ in halos with spin $\lambda = 0$, and is suppressed
by a factor $\sim 2$ for halos with $\lambda = 0.09$; (2) The main effect of
the bulge is the destruction of the harmonic core which affects the buckling;
(3) The bulge plays a minor role in the exchange of angular momentum between
the barred disk and the DM halo, during its spinup and spindown; (4) Most
interestingly, the buckling process triggers different response above/below the
disk midplane, which anti-correlates with the bulge mass; (5) In spinning
halos, the buckling process has a prolonged amplitude tail, extending by few
Gyr, as verified by measuring distortions in the Laplace plane; (6)
Furthermore, as verified by orbital spectral analysis, the bulge gains its spin
from the bar mainly via the inner Lindblad resonance, while losing it via a
number of resonances lying between the outer and inner Lindblad resonance.
