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In this paper, we present a new approach to determine the estimated time of arrival (ETA) for bus routes using (Deep) Graph Convolutional Networks (DGCNs). In addition we use the same DGCN to detect detours within a route. In our application, a classification of routes and their underlying graph structure is performed using Graph Learning. Our model leads to a fast prediction and avoids solving the vehicle routing problem (VRP) through expensive computations. Moreover, we describe how to predict travel time for all routes using the same DGCN Model. This method makes it possible not to use a more computationally intensive approximation algorithm when determining long travel times with many intermediate stops, but to use our network for an early estimate of the quality of a route. Long travel times, in our case result from the use of a call-bus system, which must distribute many passengers among several vehicles and can take them to places without a regular stop. For a case study, the rural town of Roding in Bavaria is used. Our training data for this area results from an approximation algorithm that we implemented to optimize routes, and to generate an archive of routes of varying quality simultaneously.