Very neutron-deficient 191,193Bi nuclei have been studied at the Department of Physics, University of Jyväskylä, Finland (JYFL) employing the Jurosphere II Ge-detector array coupled to the gas-filled recoil separator RITU and different tagging techniques. For the first time in heavy odd-mass nuclei, a collective band (oblate) is identified above the 2p–1h (1/2+) proton intruder state in 191Bi. In both 191,193Bi, a band based on isomeric 13/2+ state has been observed and oblate deformation for this state has been deduced.