  We exhibit a regular language of geodesics for a large set of elements of
$BS(1,n)$ and show that the growth rate of this language is the growth rate of
the group. This provides a straightforward calculation of the growth rate of
$BS(1,n)$, which was initially computed by Collins, Edjvet and Gill in [5]. Our
methods are based on those we develop in [8] to show that $BS(1,n)$ has a
positive density of elements of positive, negative and zero conjugation
curvature, as introduced by Bar-Natan, Duchin and Kropholler in [1].
