Practical ways to obtain Bode plots for an unknown circuit
You can use you DAQ equipment to inject some input signal and then capture the output signal, collect all data in a table/matrix. 

The right chapter of signal processing would be the system identification/estimation. Various methods, the recursive least squares is widely used. You would need to inject such signal that isn't repeatable over time, because any algorithm has to distinguish the which part of excitation signal caused which part of the output response. Therefore the excitation signal shall produce a result of one pulse if autocorrelated, this also means that the correlation between input and output signal would give an exact peak (lock in). 

Such signal is named PRBS (Pseudo Random Binary Sequence). You can inject this one, then use available system identification tool by calculating (and correlating) system coefficients.