  Most cool core clusters of galaxies possess active galactic nuclei (AGN) in
their centers. These AGN inflate buoyant bubbles containing non-thermal radio
emitting particles. If such bubbles efficiently confine cosmic rays (CR) then
this could explain ``radio ghosts'' seen far from cluster centers. We simulate
the diffusion of cosmic rays from buoyant bubbles inflated by AGN. Our
simulations include the effects of the anisotropic particle diffusion
introduced by magnetic fields. Our models are consistent with the X-ray
morphology of AGN bubbles, with disruption being suppressed by the magnetic
draping effect. We conclude that for such magnetic field topologies, a
substantial fraction of cosmic rays can be confined inside the bubbles on
buoyant rise timescales even when the parallel diffusivity coefficient is very
large. For isotropic diffusion at a comparable level, cosmic rays would leak
out of the bubbles too rapidly to be consistent with radio observations. Thus,
the long confinement times associated with the magnetic suppression of CR
diffusion can explain the presence of radio ghosts. We show that the partial
escape of cosmic rays is mostly confined to the wake of the rising bubbles, and
speculate that this effect could: (1) account for the excitation of the
H$\alpha$ filaments trailing behind the bubbles in the Perseus cluster, (2)
inject entropy into the metal enriched material being lifted by the bubbles
and, thus, help to displace it permanently from the cluster center and (3)
produce observable $\gamma$-rays via the interaction of the diffusing cosmic
rays with the thermal intracluster medium (ICM).
