The analysis of count processes has become an important area of research in the last two decades. In this paper we consider the simple non-negative integer-valued bilinear process INBL(1,0,1,1). The parameter estimation is addressed and the problem of forecasting integer-valued time series modeled by the INBL(1,0,1,1) process is considered. Bayesian methodology is used to obtain parameter estimates, point predictions and confidence intervals for future values of the process. The parameters estimates and predictions thus obtained are compared with their classic counterparts. The proposed approaches are illustrated with a simulation study.