Bundling and crosslinking of actin networks provide cells with tensile strength and mobility and play critical roles in diverse mechanical processes such as wounding healing and fertilization. One simple mechanism for bundling and crosslinking actin networks is using divalent counterions such as Mg²⁺ to form crossbridges between actin filaments. Counterion crossbridges can also be exploited in materials engineering to alter the mechanics of polyelectrolyte materials. As such, the mechanical properties that counterion crossbridges confer to actin networks needs to be explored. Here, we use optical tweezers microrheology to characterize the mechanical response of actin networks in the presence of varying concentrations of Mg²⁺ . We couple mechanics to structure by using confocal microscopy to characterize the mobility and architecture of networks. We show that only modest bundling and network rearrangement is required to induce dramatic increases in the elasticity and stiffness of the networks. We further show that bundles are resilient to nonlinear forcing and exhibit surprisingly minimal dissipation above a critical counterion concentration. Finally, we demonstrate that while crosslinking of network fibers plays an important role in linear regime mechanics, filament bundling dictates the nonlinear response.