  In this paper we extend the range of consistency of a constant bulk viscosity
model to redshifts up to $z\sim 8.1$. In this model the dark sector of the
cosmic substratum is a viscous fluid with pressure $p= -\zeta \theta$, where
$\theta$ is the fluid-expansion scalar and $\zeta$ is the coefficient of bulk
viscosity. Using the sample of 59 high-redshift GRBs reported by Wei (2010), we
calibrate GRBs at low redshifts with the Union 2 sample of SNe Ia, avoiding
then the circularity problem. Testing the constant bulk viscosity model with
GRBs we found the best fit for the viscosity parameter $\tilde{\zeta}$ in the
range $0<\tilde{\zeta}<3$, being so consistent with previous probes; we also
determined the deceleration parameter $q_0$ and the redshift of transition to
accelerated expansion. Besides we present an updated analysis of the model with
CMB5-year data and CMB7-year data, as well as with the baryon acoustic peak
BAO. From the statistics with CMB it turns out that the model does not describe
in a feasible way the far far epoch of recombination of the universe, but is in
very good concordance for epochs as far as $z\sim 8.1$ till present.
