The rich temporal structure of neural spike trains provides multiple dimensions to code dynamic stimuli. Popular examples are spike trains from sensory cells where bursts and isolated spikes can serve distinct coding roles. In contrast to analyses of neural coding, the cellular mechanics of burst mechanisms are typically elucidated from the neural response to static input. Bridging the mechanics of bursting with coding of dynamic stimuli is an important step in establishing theories of neural coding. Electrosensory lateral line lobe (ELL) pyramidal neurons respond to static inputs with a complex dendrite-dependent burst mechanism. Here we show that in response to dynamic broadband stimuli, these bursts lack some of the electrophysiological characteristics observed in response to static inputs. A simple leaky integrate-and-fire (LIF)-style model with a dendrite-dependent depolarizing afterpotential (DAP) is sufficient to match both the output statistics and coding performance of experimental spike trains. We use this model to investigate a simplification of interval coding where the burst interspike interval (ISI) codes for the scale of a canonical upstroke rather than a multidimensional stimulus feature. Using this stimulus reduction, we compute a quantization of the burst ISIs and the upstroke scale to show that the mutual information rate of the interval code is maximized at a moderate DAP amplitude. The combination of a reduced description of ELL pyramidal cell bursting and a simplification of the interval code increases the generality of ELL burst codes to other sensory modalities.