We examine the mechanism of bundling of cytoskeletal actin filaments by two representative bundling proteins, fascin and espin. Small-angle x-ray studies show that increased binding from linkers drives a systematic overtwist of actin filaments from their native state, which occurs in a linker-dependent fashion. Fascin bundles actin into a continuous spectrum of intermediate twist states, while espin only allows for untwisted actin filaments and fully overtwisted bundles. Based on a coarse-grained, statistical model of protein binding, we show that the interplay between binding geometry and the intrinsic flexibility of linkers mediates cooperative binding in the bundle. We attribute the respective continuous (discontinuous) bundling mechanisms of fascin (espin) to difference in the stiffness of linker bonds themselves.