On cocircuit covers of bicircular matroids

Given a graph image, one can define a matroid image on the edges image of image with circuits image where image is either the cycles of image or the bicycles of image. The former is called the cycle matroid of image and the latter the bicircular matroid of image. For each bicircular matroid image, we find a cocircuit cover of size at most the circumference of image that contains every edge at least twice. This extends the result of Neumann-Lara, Rivera-Campo and Urrutia for graphic matroids.