The changes in the mean-square charge radius (relative to ^{209}Bi), magnetic dipole, and electric quadrupole moments of ^{187,188,189,191}Bi were measured using the in-source resonance-ionization spectroscopy technique at ISOLDE (CERN). A large staggering in radii was found in ^{187,188,189}Bi^{g}, manifested by a sharp radius increase for the ground state of ^{188}Bi relative to the neighboring ^{187,189}Bi^{g}. A large isomer shift was also observed for ^{188}Bi^{m}. 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.