  Bundling crossings is a strategy which can enhance the readability of
drawings. In this paper we consider good drawings, i.e., we require that any
two edges have at most one common point which can be a common vertex or a
crossing. Our main result is that there is a polynomial time algorithm to
compute an 8-approximation of the bundled crossing number of a good drawing (up
to adding a term depending on the facial structure of the drawing). In the
special case of circular drawings the approximation factor is 8 (no extra
term), this improves upon the 10-approximation of Fink et al. (Bundled
crossings in embedded graphs, Proc. Latin'16). Our approach also works with the
same approximation factor for families of pseudosegments, i.e., curves
intersecting at most once. We also show how to compute a 9/2-approximation when
the intersection graph of the pseudosegments is bipartite.
