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Thin plastic bags are ubiquitous in retail stores, healthcare, food handling, recycling, homes, and school lunchrooms. They are challenging both for perception (due to specularities and occlusions) and for manipulation (due to the dynamics of their 3D deformable structure). We formulate the task of "bagging:" manipulating common plastic shopping bags with two handles from an unstructured initial state to an open state where at least one solid object can be inserted into the bag and lifted for transport. We propose a self-supervised learning framework where a dual-arm robot learns to recognize the handles and rim of plastic bags using UV-fluorescent markings; at execution time, the robot does not use UV markings or UV light. We propose the AutoBag algorithm, where the robot uses the learned perception model to open a plastic bag through iterative manipulation. We present novel metrics to evaluate the quality of a bag state and new motion primitives for reorienting and opening bags based on visual observations. In physical experiments, a YuMi robot using AutoBag is able to open bags and achieve a success rate of 16/30 for inserting at least one item across a variety of initial bag configurations. Supplementary material is available at https://sites.google.com/view/autobag.