The electronic absorption spectrum of the (0,2), (1,3), and (6,9) bands of the B4Sigmau(-)-X4Sigmag- system of C2+ was obtained using the velocity modulation technique in conjunction with heterodyne detection. The rotationally resolved spectrum shows perturbations, which are attributed to the 2(2)Piu state. The mixing between the B4Sigmau- state and the 2(2)Piu state for nearly degenerate levels generated enough intensity borrowing to observe twenty 2(2)Piu<--X4Sigmag- forbidden transitions. The parameters of a model Hamiltonian were fit to the bands and their corresponding forbidden transitions. Line position measurements, line strength factors, and expectation values for the orbital angular momentum Lambda' for the forbidden transitions are reported. Molecular parameters from the global fit of each band, including their corresponding forbidden transitions, are reported.