  Let $K$ be a totally real number field and let $B$ be a totally definite
quaternion algebra over $K$. In this article, given a set of representatives
for ideal classes for a maximal order in $B$, we show how to construct in an
efficient way a set of representatives of ideal classes for any Bass order in
$B$. The algorithm does not require any knowledge of class numbers, and
improves the equivalence checking process by using a simple calculation with
global units. As an application, we compute ideal classes representatives for
an order of level 30 in an algebra over the real quadratic field
$\Q[\sqrt{5}]$.
