Model fitting methods have been widely used in neuroscience to infer the parameters of a biophysical system from its responses to experimental stimulations. For instance, the parameters of a chemical synapse (e.g. the number of presynaptic vesicles, or its depression time constant) can be estimated from its postsynaptic responses to evoked stimuli. However, these estimates critically depend on the stimulation protocol being used. Experiments are often conducted with non-adaptive stimulation protocols that may not yield enough information about these parameters. Here, we propose using Bayesian active learning (BAL) for synaptic characterization, and to choose the most informative stimuli by maximizing the mutual information between the data and the unknown parameters. This requires performing high-dimensional integration and optimization in real time. Current methods are either too time consuming, or only applicable to specific models. We build on recent developments in non-linear filtering and parallel computing to provide a general framework for online BAL, which is fast enough to be used in real-time biological experiments and can be applied to a wide range of statistical models. Using synthetic data, we show that our method has the potential to significantly improve the precision of inferred synaptic parameters. Finally, we explore the situation where the constraint is not given by the total number of observations but by the duration of the experiment.