Detailed magnetoreflection studies on the binary and bisectrix faces of bismuth are made to look for the fine structure predicted by the Baraff generalization of the Lax two-band model. This generalization is required to explain certain structure in the de Haas-van Alphen data. No fine structure is found experimentally in the magnetoreflection spectra for these optical faces. Magnetoreflection data were also taken for H--> in the trigonal direction to look for expected departures from the Lax model. No such departures were found. By assuming a particularly simple form for the Baraff Hamiltonian, it is possible to explain both the magnetoreflection and de Haas-van Alphen data, which had previously been thought to be inconsistent.