We present an θ(|S|·|E_G|) deterministic construction heuristic for the Asymmetric Traveling Salesman Problem ATSP on digraphs G. The heuristic relies on the fast determination of an approximate bidirectional Steiner Tree with respect to the stopovers S⊆V_G. The algorithm is a robust and very fast general ATSP-solution method. It has an astonishing approximation ε ≈ 0.05 and is therefore especially appropriate for online and real-time navigation applications with a high number of stopovers and where graph changes have to be considered just in time. It turns out that the proposed method is a new serious competitor for all existing ATSP heuristics, especially qualified for navigation apps of large problem sizes that depend on the tours' real-time calculation instantly executed on online graphs while observing turn restrictions.