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The standard formulation of General Relativity Theory, in the absence of a cosmological constant, is unable to explain the responsible mechanism for the observed late-time cosmic acceleration. On the other hand, by inserting the cosmological constant in Einstein's field equations it is possible to describe the cosmic acceleration, but the cosmological constant suffers from an unprecedented fine-tunning problem. This motivates one to modify Einstein's space-time geometry of General Relativity. The $f(Q)$ modified theory of gravity is an alternative theory to General Relativity, where the non-metricity scalar $Q$ is the responsible candidate for gravitational interactions. In the present work we consider a Friedmann-Lemâitre-Robertson-Walker cosmological model dominated by bulk viscous cosmic fluid in $f(Q)$ gravity with the functional form $f(Q)=αQ^n$, where $α$ and $n$ are free parameters of the model. We constrain our model with the recent Pantheon supernovae data set of 1048 data points, Hubble data set of 31 data points and baryon acoustic oscillations data set consisting of six points. For higher values of redshift, it is clear that the $f(Q)$ cosmology better fits data than standard cosmology. We present the evolution of our deceleration parameter with redshift and it properly predicts a transition from decelerated to accelerated phases of the universe expansion. Also, we present the evolution of density, bulk viscous pressure and the effective equation of state parameter with redshift. Those show that bulk viscosity in a cosmic fluid is a valid candidate to acquire the negative pressure to drive the cosmic expansion efficiently.We also examine the behavior of different energy conditions to test the viability of our cosmological $f(Q)$ model. Furthermore, the statefinder diagnostics are also investigated in order to distinguish among different dark energy models.