This paper demonstrates how an efficient representation of the planned path using B-splines, and a construction procedure that takes advantage of the neural network's inductive bias, speed up both the inference and training of a DNN-based motion planner. We build upon our recent work on learning local car maneuvers from past experience using a DNN architecture, introducing a novel B-spline path construction method, making it possible to generate local maneuvers in almost constant time of about 11 ms, respecting a number of constraints imposed by the environment map and the kinematics of a car-like vehicle. We evaluate thoroughly the new planner employing the recent Bench-MR framework to obtain quantitative results showing that our method outperforms stateof-the-art planners by a large margin in the considered task.