The electron-hole (EH) Bilayer Tunneling Field-Effect Transistor promises to eliminate heavy-doping band-tails enabling a smaller subthreshold swing voltage. Nevertheless, the electrostatics of a thin structure must be optimized for gate efficiency. We analyze the tradeoff between gate efficiency versus on-state conductance to find the optimal device design. Once the EH Bilayer is optimized for a given on-state conductance, Si, Ge, and InAs all have similar gate efficiency, around 40-50%. Unlike Si & Ge, only the InAs case allows a manageable work function difference for EH Bilayer Transistor operation.