Managing electric bus (EB) fleets at scale introduces operational challenges that differ fundamentally from those of conventional fuel-powered fleets. A main challenge is the need to jointly coordinate parking, recharging, and service dispatching under tight time and infrastructure constraints while accounting for uncertainty in energy consumption. We consider an indoor depot layout with parallel FIFO lanes and a limited number of simultaneous chargers (a configuration used in Canada and other Nordic countries). For this setting, we formulate the resulting real-time electric bus parking, charging, and dispatching problem as a mixed-integer linear program solved at each EB arrival within a sliding-window framework. To account for systematic errors in energy consumption predictions, we introduce a tracking signal algorithm, based on a backward cumulative sum scheme, that continuously monitors energy consumption prediction errors and dynamically adjusts arrival state-of-charge predictions for future EBs. Computational experiments on instances with up to four lanes and twelve spots per lane, covering 1,500 stochastic scenarios across five energy consumption regimes, show that the adaptive approach reduces reserve bus deployments by up to 55.6% relative to a static forecasting baseline. It also improves solution quality by up to 27.9%, without increasing computational times.