I know that this topic is a bit old but maybe it could help...
I needed some fast poor man's Bode plots and I always has been using the FFT + persistence.
For the input, instead of frequency sweeping, if used white noise; it could be easier and faster due to the broad band spectrum nature, therefore, the input frequencies you try are more than with the frequency sweep (due to the finite frequency step size) and if the persistence mode is really short, you have chance to see really quick the Bode plot over more frequencies. At the end, it is the same idea as random sampling instead of uniform.
The only thing to remember is that, as the white noise should has zero means, the characterization at near DC frequencies is not valid.
I hope it can helps to anyone in a hurry