  The article communicates an alternative route to suffice the late-time
acceleration considering a bulk viscous fluid with viscosity coefficient $\zeta
=\zeta _{0}+ \zeta _{1} H + \zeta _{2} H^{2}$, where $\zeta _{0}, \zeta _{1},
\zeta _{2}$ are constants in the framework of $f(R,T)$ modified gravity. We
presume the $f(R,T)$ functional form to be $f=R+2\alpha T$ where $\alpha$ is a
constant. We then solve the field equations for the Hubble Parameter and study
the cosmological dynamics of kinematic variables such as deceleration, jerk,
snap and lerk parameters as a function of cosmic time. We observe the
deceleration parameter to be highly sensitive to $\alpha$ and undergoes a
signature flipping at around $t\sim 10$ Gyrs for $\alpha=-0.179$ which is
favored by observations. The EoS parameter for our model assumes values close
to $-1$ at $t_{0}=13.7$Gyrs which is in remarkable agreement with the latest
Planck measurements. Next, we study the evolution of energy conditions and find
that our model violate the Strong Energy Condition in order to explain the
late-time cosmic acceleration. To understand the nature of dark energy mimicked
by the bulk viscous baryonic fluid, we perform some geometrical diagnostics
like the $\{r,s\}$ and $\{r,q\}$ plane. We found the model to mimic the nature
of a Chaplygin gas type dark energy model at early times while a Quintessence
type in distant future. Finally, we study the violation of continuity equation
for our model and show that in order to explain the cosmic acceleration at the
present epoch, energy-momentum must violate.
