BodePlot[(1 + s/10^6)/((1 + s/10^2) (1 + s/10^12)), {10, 10^20}]

The second argument should be the frequency range (horizontal axis). If you use PlotRange, that affects the vertical axis, which is not what you want. Refer to the documentation:

?BodePlot

BodePlot[(1 + s/10^6)/((1 + s/10^2) (1 + s/10^12)), {10, 10^20}]

The second argument should be the frequency range (horizontal axis). If you use PlotRange, that affects the vertical axis, which is not what you want. Refer to the documentation:

?BodePlot

In response to your follow-up request, try these options:

BodePlot[(1 + s/10^6)/((1 + s/10^2) (1 + s/10^12)), {.1, 10^20},
     PlotRange -> {{-150, 50}, {-180, 90}}, Axes -> True, Frame -> False, 
     AxesOrigin -> {{0, 0.1}, {0, 0.1}}]

The thing to understand about the default output of BodePlot is that it plots two graphs, and the vertical scale on each is different; therefore, when supplying plotting options, they must be given as a list.