Interactions of multiple molecular motors with bundles of actin and microtubule filaments form the basis for many cytoskeletal processes including axonal growth, muscle contraction, cell division and platelet formation. Continuum models based on generalized diffusion equations have been suggested to quantify the dynamics of such active bundles. In highly cross-linked and densely packed filament bundles, however, a major complication arises due to the multiple interactions that each filament forms with its neighbors. To explore the effects of these interactions, we used detailed computer simulations and studied the bundles with different types of motors at different densities and boundary conditions. We found that highly cross-linked bundles exhibit effects of long-ranged interactions that are sensitive to the boundary conditions. In open bundles, these give rise to 'telescopic' patterns resulting in significant acceleration of the filaments at the edges. In contrast, in ringed bundles, the long-ranged interactions 'lock' filaments and slow down their movements. The filaments in loosely connected bundles, on the other hand, undergo local diffusion-drift dynamics consistent with previous continuum models. Our simulations also demonstrate the sorting phenomena in the mixed-polarity bundles and reveal characteristic scales and conditions for spontaneous pattern formation in the bundle. We discuss the relevance of our results for cytoskeleton systems such as microtubules in axons, platelet formation, kinetochore fibers and actin bundles in motile cells.