  We present Suzaku X-ray observations along two edge regions of the Fermi
Bubbles, with eight ~20 ksec pointings across the northern part of the North
Polar Spur (NPS) surrounding the north bubble and six across the southernmost
edge of the south bubble. After removing compact X-ray features, diffuse X-ray
emission is clearly detected and is well reproduced by a three-component
spectral model consisting of unabsorbed thermal emission (temperature kT ~0.1
keV from the Local Bubble (LB), absorbed kT ~0.3 keV thermal emission related
to the NPS and/or Galactic Halo (GH), and a power-law component at a level
consistent with the cosmic X-ray background. The emission measure (EM) of the
0.3 keV plasma decreases by ~50% toward the inner regions of the north-east
bubble, with no accompanying temperature change. However, such a jump in the EM
is not clearly seen in the south bubble data. While it is unclear if the NPS
originates from a nearby supernova remnant or is related to previous activity
within/around the Galactic Center, our Suzaku observations provide evidence
suggestive of the latter scenario. In the latter framework, the presence of a
large amount of neutral matter absorbing the X-ray emission as well as the
existence of the kT ~ 0.3 keV gas can be naturally interpreted as a weak shock
driven by the bubbles' expansion in the surrounding medium, with velocity v_exp
~300 km/s (corresponding to shock Mach number M ~1.5), compressing the GH gas
to form the NPS feature. We also derived an upper limit for any non-thermal
X-ray emission component associated with the bubbles and demonstrate, that in
agreement with the findings above, the non-thermal pressure and energy
estimated from a one-zone leptonic model of its broad-band spectrum, are in
rough equilibrium with that of the surrounding thermal plasma.
