The \sim 200 H i clouds observed to be entrained in the Fermi Bubble wind show a trend of increasing maximum | { V _ { \mathrm { LSR } } } | with Galactic latitude . We analyze previous observations and present new data from the Green Bank Telescope that rule out systematic effects as the source of this phenomenon . Instead , it is likely evidence for acceleration of the clouds . The data suggest that clouds in the lower 2 kpc of the Fermi Bubbles , within the Bubble boundaries established from X-ray studies , have an outflow velocity that rises from \approx 150 - 200 km s ^ { -1 } close to the Galactic Center and reaches \approx 330 km s ^ { -1 } at a distance of 2.5 - 3.5 kpc . These parameters are also consistent with the kinematics of UV absorption lines from highly ionized species observed against two targets behind the Fermi Bubbles at b = -6 \fdg 6 and b = +11 \fdg 2 . The implied neutral cloud lifetime is 4 – 10 Myr .