High-spin states in the doubly-odd 198 Bi nucleus have been studied by using the 185,187 Re( 16 O, xn) reactions at the beam energy of 112.5 MeV. γ − γ coincidences, directional correlation ratio and integrated polarization asymmetry ratio were measured by using the INGA array with 15 Comptonsuppressed clover HPGe detectors. Definite spins and parities were assigned to the observed levels. The high-spin structure is grouped into three bands (B1, B2 and B3), of which two (B1 and B2) exhibit the properties of magnetic rotation (MR). Tilted axis cranking calculations were carried out to explain the MR bands having large multi-quasiparticle (qp) configurations. The calculated results explain the bands B1 and B2 very nicely, confirming the shears mechanism and suggest a crossing of two MR bands in both the cases. The crossing is from 6-qp to 8-qp in band B1 and from 4-qp to 6-qp in band B2, a very rare finding. A semiclassical model has also been used to obtain the particle-hole interaction strengths below the band-crossing for the bands B1 and B2.