A bode plot is by definition a drawing with the poles and zeroes of the transfer function of a system.
What you want to do is called the Frequency/Phase response of your system.
Without the pole/zero data, it is of course possible. The process goes something like this:
You sweep a sine over your wanted frequency range, and from FFT, you get the Frequency magnitude and phase for each frequency measured.
then you make two plots, one with log Frequency / Amplitude, and with with log Frequency / Phase.
And there you have your Frequency / Phase response.
Old analog instruments used a sine sweep and a peak detector for amplitude, instead of FFT, very cool, but a bit tricky to get the phase response.
