Intruder state excitation energies in odd-mass nuclei just outside a closed proton shell plotted versus neutron number generally exhibit parabola-shaped curves with minima near neutron mid-shells. The Bi isotopes, however, do not seem to follow this trend. Recent experiments performed at Argonne National Laboratory have identified the previously unobserved {sup 187}Bi ground state (h{sub 9/2}) to {sup 183}TI ground state s{sub 1/2} {alpha} transition. Its energy when combined with those of two earlier known transitions, namely {sup 187}Bi (h{sub 9/2}) {yields} {sup 183m}Tl (h{sub 9/2}) and {sup 187m}Bi (s{sub 1/2}) {yields} {sup 183}Tl(s{sub 1/2}), establishes the excitation energies of the {sup 183m}Tl and {sup 187m}Bi to be 620(20) keV and 110(20) keV, respectively. This value for {sup 187m}Bi is 80 keV lower than the excitation energy of the same intruder level in {sup 189}Bi. Implications of this result with respect to intruder-state systematics are discussed