The response of bursting neurons to fluctuating inputs is usually hard to predict, due to their strong nonlinearity. For the same reason, decoding the injected stimulus from the activity of a bursting neuron is generally difficult. In this paper we propose a method describing (for neuron models) a mechanism of phase coding relating the burst onsets with the phase profile of the input current. This relation suggests that burst onset may provide a way for postsynaptic neurons to track the input phase. Moreover, we define a method of phase decoding to solve the inverse problem and estimate the likelihood of burst onset given the input state. Both methods are presented here in a unified framework, describing a complete coding-decoding procedure. This procedure is tested by using different neuron models, stimulated with different inputs (stochastic, sinusoidal, up, and down states). The results obtained show the efficacy and broad range of application of the proposed methods. Possible applications range from the study of sensory information processing, in which phase-of-firing codes are known to play a crucial role, to clinical applications such as deep brain stimulation, helping to design stimuli in order to trigger or prevent neural bursting.