Density functional calculations including long-range dispersion effects demonstrate that non-covalent doping with an electron donor acceptor couple of molecules can open an energy gap in a bilayer graphene. The band gap modulation can be controlled not only by the choice of adsorbed molecules (n-dopant versus p-dopant) but also by their concentration. A deep analysis of the charge transfer reveals that charge redistribution in bilayer graphene is the key issue for gap opening, due to the induced inversion symmetry breaking. The dual molecular non-covalent doping mode can achieve the opening of a gap up to 138 meV.