Feedback linearization suffers from a number of restrictions which have limited its use in model-based predictive control. Some of these restrictions do not apply to the case of bilinear systems, but problems with input constraints and unstable zero dynamics persist. This paper overcomes these difficulties by means of an interpolation strategy. Involved in this interpolation is a stabilizing trajectory which is computed through the use of invariant feasible sets (defined for the bilinear model) and a more aggressive trajectory which can be chosen to be either the unconstrained optimal trajectory or an alternative which guarantees that the state vector remains bounded and that the output converges to the origin.