Visible light communication (VLC) provides an alternative underwater wireless connectivity solution with its low latency and high data rates albeit at relatively shorter distances in the order of tens of meters. In the context of underwater sensor networks (USNs), VLC is particularly suitable to establish connectivity between 'data mule' autonomous underwater vehicles (AUVs) and sensor nodes since communications is enabled only when the sensor node and mule AUV are in close proximity. In this paper, we consider a USN scenario where a solar-powered AUV gathers data from the sensor nodes using VLC signaling. We formulate a three-dimensional trajectory optimization for solar-powered AUVs with the goal of maximizing the harvested energy under constraints imposed by the data transmission. The optimization constraints include the minimum required data transfer rate, therefore a corresponding transmission distance, between the sensors and the AUV. We formulate the problem as a bilevel optimization problem. The lower-level objective function is in the form of traveling salesman problem which determines the optimum sequence order of the sensor nodes to be visited while the upper-level objective function is the optimization of the trajectory between each pair of adjacent nodes for the given order of node visits. Our numerical results demonstrate that the proposed trajectory significantly prolongs the mission time and autonomous operation of the AUV without the need to return to home base. Furthermore, since the proposed trajectory optimization is reactive to ocean currents, it brings reductions in the energy consumption of the AUVs.