A broad collection of technologies, including e.g. drug metabolism, biofuel combustion, photochemical decontamination of water, and interfacial passivation in energy production/storage systems rely on chemical processes that involve bond-breaking molecular reactions. In this context, a fundamental thermodynamic property of interest is the bond dissociation energy (BDE) which measures the strength of a chemical bond. Fast and accurate prediction of BDEs for arbitrary molecules would lay the groundwork for data-driven projections of complex reaction cascades and hence a deeper understanding of these critical chemical processes and, ultimately, how to reverse design them. In this paper, we propose a chemically inspired graph neural network machine learning model, BonDNet, for the rapid and accurate prediction of BDEs. BonDNet maps the difference between the molecular representations of the reactants and products to the reaction BDE. Because of the use of this difference representation and the introduction of global features, including molecular charge, it is the first machine learning model capable of predicting both homolytic and heterolytic BDEs for molecules of any charge. To test the model, we have constructed a dataset of both homolytic and heterolytic BDEs for neutral and charged (-1 and +1) molecules. BonDNet achieves a mean absolute error (MAE) of 0.022 eV for unseen test data, significantly below chemical accuracy (0.043 eV). Besides the ability to handle complex bond dissociation reactions that no previous model could consider, BonDNet distinguishes itself even in only predicting homolytic BDEs for neutral molecules; it achieves an MAE of 0.020 eV on the PubChem BDE dataset, a 20% improvement over the previous best performing model. We gain additional insight into the model's predictions by analyzing the patterns in the features representing the molecules and the bond dissociation reactions, which are qualitatively consistent with chemical rules and intuition. BonDNet is just one application of our general approach to representing and learning chemical reactivity, and it could be easily extended to the prediction of other reaction properties in the future.