We investigate two single-photon generation schemes and compare their suitability for use in time-bin entanglement encoding. A trapped ion coupled to an optical cavity produces single photons through a cavity-assisted Raman transition. By manipulating the phase relationship between time-bins of successive photons, distinct features in the interference pattern of a Hong–Ou–Mandel measurement emerge. Through careful selection of the initial state, detrimental effects of spontaneous emission can be significantly reduced. We demonstrate that this reduction allows us to impart a measurable phase profile onto the emitted photons making time-bin entanglement encoding feasible with an ion-cavity system.