Qualitatively assessing time domain characteristics from bode plot
The response of a system is related to it's poles and zeros and static gains (transfer functions), which comes from the system's characteristic equation.

Also, there are plenty of info in the internet concerning how to "draw" a bode plot from a transfer function. For instance, a pole corresponds to a -3db gain decay from its frequency. Then if you look a bode plot and its gain only starts decaying on high frequencies, then you can assume you have fast poles and the time response will be fast.

So there's this relation:

characteristic equation &lt;-> Transfer function &lt;-> bode plot

So you can come from a bode plot, have an understanding about poles and zeros of the system's transfer function, then from here you can estimate settling time from the well known formulae.