On cocircuit covers of bicircular matroids

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