It has been shown that the sensitivity of FET-based biosensors is highest when the biosensor is biased in the subthreshold regime. Given a substrate contact and a solution electrode, there is a wide range of voltages that bias the sensor this way, and not all of them are optimal; we use simulations to clarify the proper bias point. We also show that screening in the buffer solution is bias dependent, and we describe the origin of this dependence. Furthermore, we show that phenomena in the FET part and screening at the outer surface of the biosensor may have differing optimization criteria in terms of biasing. To make the most of the biosensor, both have to be optimized simultaneously. We show that this may require engineering of the charges at the surface of the biosensor, possibly affecting the choice of receptor molecules, linker molecules, and insulator material.