Hyperfine splitting in Bi 82+ and Pb 81+ ions was calculated using continuum RPA approach with effective residual forces. To fix the parameters of the theory the nuclear magnetic dipole moments of two one-particle and two one-hole nuclei around 208 Pb were calculated using the same approach. The contribution from velocity dependent two-body spin-orbit residual interaction was calculated explicitly. Additionally, the octupole moment of 209 Bi and the hfs in muonic bismuth atom were calculated as well in the same approach. All the calculated observables, except the electronic hfs in 209 Bi, are in good agreement with the data. We argue for more accurate measurement of the octupole moment and the muonic hfs for 209 Bi.