Successful wireless communication requires that sender and receiver are operational at the same time. This requirement is difficult to satisfy in battery-free networks, where the energy harvested from ambient sources varies across time and space and is often too weak to continuously power the devices. We present Bonito, the first connection protocol for battery-free systems that enables reliable and efficient bi-directional communication between intermittently powered nodes. We collect and analyze real-world energy-harvesting traces from five diverse scenarios involving solar panels and piezoelectric harvesters, and find that the nodes' charging times approximately follow well-known distributions. Bonito learns a model of these distributions online and adapts the nodes' wake-up times so that sender and receiver are operational at the same time, enabling successful communication. Experiments with battery-free prototype nodes built from off-the-shelf hardware components demonstrate that our design improves the average throughput by 10-80× compared with the state of the art.