The attachment of electrons to large helium droplets containing up to 10(8) atoms produced in supercritical liquid free jet expansions has been investigated in a crossed beam scattering experiment. Negative cluster ions were formed in collisions with electrons from a nearly monoenergetic (delta E approximate to 0.25 eV) electron beam with energies E-el = 1.0-100 eV and were subsequently size selected by electrostatic deflection. Depending on the droplet size up to seven distinct resonancelike maxima in the negative-ion signal with peak widths Delta E-1/2 proportional to the droplet radius could be resolved. The lowest energy peak at E-e1 = 1.8-2.3 eV depending on size, is attributed to a direct localization of the electron which subsequently creates a bubble inside the He droplet. The sharp additional peaks at energies above 20 eV are explained by the thresholds for single or successive electronic excitations of the droplets which result in a zero-kinetic-energy electron which then also localizes in an internal bubble.