  In this manuscript, we analyze the viscous fluid cosmological model in the
framework of recently proposed $f(Q)$ gravity by assuming three different forms
of bulk viscosity coefficients, specifically, $(i)\zeta
=\zeta_{0}+\zeta_{1}\left( \frac{\dot{a}}{a}\right) +\zeta_{2}\left(
\frac{{\ddot{a}}}{\dot{a}}\right) $, $(ii)\zeta =\zeta_{0}+\zeta_{1}\left(
\frac{\dot{a}}{a}\right)$, and $(iii)\zeta =\zeta_{0}$ and a linear $f(Q)$
model, particularly, $f(Q)=\alpha Q$ where $\alpha \neq 0$ is free model
parameter. We estimate the bulk viscosity coefficients and the model parameter
values using the combined H(z)+Pantheon+BAO data set. We study the asymptotic
behavior of our cosmological bulk viscous model by utilizing the phase space
method. We find that corresponding to all three cases, our model depicts the
evolution of the universe from matter dominated decelerated epoch (a past
attractor) to a stable de-sitter accelerated epoch (a future attractor).
Further, we study the physical behavior of effective pressure, effective
equation of state (EoS), and the statefinder parameters. We find that the
pressure component in the presence of bulk viscosity shows negative behavior
and the effective EoS parameter predicts the accelerated expansion phase of the
universe for all three cases. Moreover, we obtain that the trajectories of our
model lie in the quintessence region and it converges to the $\Lambda$CDM fixed
point in the far future. We find that the accelerated deSitter like phase comes
purely from the $\bar{\zeta}_0$ case without any geometrical modification to
GR. Moreover, we find that the late-time behavior of all three cases of
viscosity coefficients are identical.
