In this note, we investigate the controllability of linear hybrid systems via bumpless transfer input and constrained switching. By bumpless transfer input, we mean that the control input signals are as close as possible at switching times. By constrained switching, we mean that the switching index sequence is cyclic and the switching time sequence is possibly with pre-assigned duration intervals. While the problem is well motivated in several practical situations, it is also theoretically interesting. A complete criterion for controllability is presented, and a computational procedure is developed for finding a switching signal and a control input to achieve the controllability.