The neutron spallation cross sections of 12C and 209Bi have been measured in the quasi-monoenergetic p-7Li neutron fields in the 20- and 150-MeV energy range. The irradiation experiments were performed at four cyclotron facilities: (a) the Institute for Nuclear Study (INS), University of Tokyo; (b) the Cyclotron and Radioisotope Center, Tohoku University; (c) the Takasaki Research Establishment (TIARA), Japan Atomic Energy Research Institute; and (d) the Institute of Physical and Chemical Research (RIKEN). The neutron spectrum has been measured with the time-of-flight method using an organic liquid scintillator, and the absolute value of peak neutron fluence has been estimated from the activation method of lithium target at INS, RIKEN, and the proton recoil counter telescope at TIARA. The cross-section data of 12C(n,2n)11C and 209Bi(n,xn) (x = 3,12) reactions are reported. Our experimental data were compared with other experimental data [only for 12C(n,2n)11C and 209Bi(n,3n)207Bi reactions] and the ENDF/B-VI high-energy file data. The comparison showed good agreement between our data and others. Our data of 209Bi(n,xn) reactions above 20 MeV and of 12C(n,2n)11C reactions above 40 MeV are the first experimental data and will be applied to high-energy neutron spectrometry for the Bi spallation detector.