Bounded response variables such as percentages, proportions, or rates are common in applications involving social and educational datasets, including rates of poverty or rates of achievement by municipalities, counties or provinces. New regression models have been proposed in recent years by considering distributions such as the Beta, Simplex and Ku-maraswamy models for this type of data. However, to this type of dataset, it is common to observe the spatial dependence of units. For instance, municipalities or counties are organized into states. For this case, the supposition of independence among observations in the same state removes relevant relations between neighboring provinces. In this paper, we present a model of spatially bounded distribution regression with a Bayesian estimation approach where spatial relations are modeled by a spatial random variable with a particular dependence structure, such as the intrinsic conditional autoregressive model or the Leroux definition. Additionally, the Bayesian inferential method and model comparison criteria are discussed. Simulation studies and an application in reading comprehension spatial data are used to illustrate the performance of the proposed model and the estimation method adopted.