  The dynamics of magnetic bubble solitons in a two-dimensional isotropic
antiferromagnetic spin lattice is studied, in the case where the exchange
integral J(x,y) is position dependent. In the near continuum regime, this
system is described by the relativistic O(3) sigma model on a spacetime with a
spatially inhomogeneous metric, determined by J. The geodesic approximation is
used to describe low energy soliton dynamics in this system: n-soliton motion
is approximated by geodesic motion in the moduli space of static n-solitons,
equipped with the L^2 metric. Explicit formulae for this metric for various
natural choices of J(x,y) are obtained. From these it is shown that single
soliton trajectories experience refraction, with 1/J analogous to the
refractive index, and that this refraction effect allows the construction of
simple bubble lenses and bubble guides. The case where J has a disk
inhomogeneity (taking the value J_1 outside a disk, and J_2<J_1 inside) is
considered in detail. It is argued that, for sufficiently large J_1/J_2 this
type of antiferromagnet supports approximate quasibreathers: two or more
coincident bubbles confined within the disk which spin internally while their
shape undergoes periodic oscillations with a generically incommensurate period.
