The bias-dependent signal transmission of flexible synaptic transistors is investigated. The novel neuromorphic devices are fabricated on a thin and transparent plastic sheet, incorporating a high-performance organic semiconductor, dinaphtho[2,3-b:2′,3′-f]thieno[3,2-b]thiophene, into the active channel. Upon spike emulation at different synaptic voltages, the short-term plasticity feature of the devices is substantially modulated. By adopting an iterative model for the synaptic output currents, key physical parameters associated with the charge carrier dynamics are estimated. The correlative extraction approach is found to yield the close fits to the experimental results, and the systematic evolution of the timing constants is rationalized.