I have come up with one method.

tfm = TransferFunctionModel[{{1/(s + 100)/(s + 10000)}}, s]

{mag, phase} = 
 BodePlot[tfm, PlotLabel -> {"Mag", "Phase"}, 
  ImageMargins -> {{{5, 5}, {5, 5}}, {{10, 10}, {10, 10}}}, 
  PlotLayout -> "List"]

bplt2 = GraphicsColumn[{mag, phase}, 
  ImageMargins -> {{20, 20}, {20, 10}}, 
  PlotLabel -> Style["Bode Plot", 20], ImageSize -> {8.5, 11} 72]

Export["bp10.pdf", 
 Rasterize[bplt2, ImageResolution -> 100, ImageSize -> {8.5, 11} 72],ImageResolution->100]

Here BodePlot provides separate mag and phase graphics. They are combined with GraphicsColumn into a desirable image, and then exported as a rasterized PDF. The PDF appears to be at 300dpi rather than the 100 specified.