<p>Telecomputation via non-local implementation of quantum gates between spatially separated processors is crucial for realizing scalable quantum networks and distributed quantum computing. In this regard, an efficient theoretical protocol for bidirectional teleportation of controlled unitary <i>(cU)</i> gates is presented. The proposed protocol enables the implementation of controlled unitary gates in both directions between two remote quantum processors. Furthermore, this protocol requires one ebit, which is the minimum quantum cost for quantum gate teleportation. This represents an improvement over existing approaches, which either enable only unidirectional gate implementation or require a high quantum resource cost. The efficiency of the teleportation protocol is quantified through fidelity, which is considered a gate-error quantifier in our context. Additionally, we provide a noise analysis by considering that the entangled channel is affected by a generalized amplitude damping channel (<i>GADc</i>). Our findings show that by controlling GADc probabilities, optimal bidirectional teleportation of <i>cU</i> gates can be achieved. These results establish our protocol as a promising candidate for noise-resilient, low-cost bidirectional cU gate implementation in distributed quantum architectures.</p>