The changes in the mean-square charge radius (relative to Bi209), magnetic dipole, and electric quadrupole moments of Bi187,188,189,191 were measured using the in-source resonance-ionization spectroscopy technique at ISOLDE (CERN). A large staggering in radii was found in Bi187,188,189g, manifested by a sharp radius increase for the ground state of Bi188 relative to the neighboring Bi187,189g. A large isomer shift was also observed for Bi188m. Both effects happen at the same neutron number, N=105, where the shape staggering and a similar isomer shift were observed in the mercury isotopes. Experimental results are reproduced by mean-field calculations where the ground or isomeric states were identified by the blocked quasiparticle configuration compatible with the observed spin, parity, and magnetic moment.