The elastic scattering of electrons in atomic helium assisted by a bichromatic laser field is investigated in the second order Bo approximation. The target atom is approximated by a simple screening potential. The dependence of the differential cross section on the relative phase between the two laser components is calculated, and compared with the recent results of first order Bo approximation [Sun J F, Liang M C and Zhu Z L 2007Chin. Phys. Lett. 24 2572].