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Quantum algorithms are promising candidates for the enhancement of computational efficiency for a variety of computational tasks, allowing for the numerical study of physical systems intractable to classical computers. In the Noisy Intermediate Scale Quantum (NISQ) era of quantum computing, however, quantum resources are limited and thus quantum algorithms utilizing such resources efficiently are highly coveted. We present a resource-efficient quantum algorithm for bosonic quantum simulations using the Variational Quantum Eigensolver algorithm with the Unitary Coupled Cluster ansatz. Our algorithm proves to significantly increase accuracy with a simultaneous large reduction of required quantum resources, exhibiting increased performance for all relevant parameters compared to current approaches. It provides a shorter route to achieve a quantum advantage in bosonic quantum simulations along with a flexible method to tailor the utilized quantum resources of a quantum computer. While being specifically feasible for NISQ devices, the advantages of our algorithm are independent of hardware parameters, maintaining its superiority for future fault-tolerant quantum devices. The study of vibrational properties of molecular systems is crucial in a variety of contexts, such as spectroscopy, fluorescence, chemical reaction dynamics and transport properties. Thus, our algorithm provides a resourceefficient flexible approach to study such applications in the context of quantum computational chemistry on quantum computers.