Isotope shifts and hyperfine structures of the bismuth isotope chain have been studied on the 306.7 nm line in off-line measurements using gas cell laser spectroscopy and atomic beam spectroscopy. The changes in nuclear mean square charge radii and the nuclear magnetic and spectroscopic quadrupole moments have been deduced. The neutron-rich isotopes are the first isotones of Pb to be measured immediately above the N=126 shell closure. A remarkable correspondence between the nuclear charge radii of the Bi and Pb isotope chains is demonstrated by a King Plot analysis. The relationship between nuclear shapes and the charge radii can be understood in the framework of the spherical shell model using few-nucleon configurations.