Quantum coupling between mechanical oscillators and atomic gases generating entanglement has been recently experimentally demonstrated using their subsequent interaction with light. The next step is to build a hybrid atom-mechanical quantum gate showing bosonic interference effects of single quanta in the atoms and oscillators. We propose an experimental test of Hong-Ou-Mandel interference between single phononic excitation and single collective excitation of atoms using the optical connection between them. A single optical pulse is sufficient to build a hybrid quantum-nondemolition gate to observe the bunching of such different quanta. The output atomic-mechanical state exhibits a probability of a hybrid bunching effect that proves its nonclassical aspects. This proposal opens a feasible road to broadly test such advanced quantum bunching phenomena in a hybrid system with different specific couplings.