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Computations with quantum harmonic oscillators, or qumodes, represents a promising and rapidly evolving approach for quantum computing. Unlike qubits, which are two-level quantum systems, bosonic qumodes can have an infinite number of discrete levels, and can also be represented using continuous-variable bases. One of the most promising applications of quantum computing is the simulation of many-fermion problems, such as those encountered in molecular electronic structure calculations. In this work, we demonstrate how an electronic structure Hamiltonian can be transformed into a system of qumodes through qubit-assisted fermion-to-qumode mapping. After mapping the electronic structure Hamiltonian to a qubit Hamiltonian, we show how to represent it as a linear combination of bosonic gates, which can be universally controlled by qubits. We illustrate the potential of this mapping by applying it to the dihydrogen molecule, mapping the four-qubit Hamiltonian to a qubit-qumode system. The preparation of the trial qumode state and the computation of the expectation value are achieved by coupling the mapped qubit-qumode system with an ancilla qubit. This enables the formulation of bosonic variational quantum eigensolver (VQE) algorithms, such as those on hybrid qubit-qumode gates like echoed conditional displacement (ECD-VQE) or selective number-dependent arbitrary phase (SNAP-VQE), to determine the ground state of the dihydrogen molecule. In circuit quantum electrodynamics (cQED) hardware, these methods can be efficiently implemented using a microwave resonator coupled to two superconducting transmon qubits. We anticipate the reported work will pave the way for simulating many-fermion systems by leveraging the potential of hybrid qubit-qumode quantum devices.