In this paper, we consider an indoor downlink dual-hop hybrid visible light communication (VLC)/radio frequency (RF) scenario. For each transmission block, we dynamically allocate a portion of time resources to VLC and the other portion to RF transmission. In the first phase (i.e., VLC transmission), the LED carries both data and energy to an energy harvester relay node. In the second phase (i.e., RF communication), the relay utilizes the harvested energy to re-transmit the decoded information to the far RF user. During this phase, the LED continues to transmit power (no information) to the relay node, aiming to harvest energy that can be used in the next transmission block. We formulate the optimization problem in the sense of maximizing the data rate under the assumption of decode-and-forward (DF) relaying. As the design parameters, the direct current (DC) bias and the assigned time duration for VLC transmission are taken into account. In particular, the joint non-convex optimization is split into two sub-problems, which are then cyclically solved. In the first sub-problem, we fix the assigned time duration to VLC link and utilize the majorization-minimization (MM) procedure to solve the non-convex DC bias problem. In the second sub-problem, we fix the DC bias obtained in the previous step and solve the optimization problem for the assigned VLC link time duration. Our results demonstrate that a higher data rate can be achieved by solving the joint problem of DC bias and time duration compared to solely optimizing the DC bias.