A universal mounting bracket for a bicycle rack includes a pair of upstanding members extending from opposite sides of a base member. Each upstanding member includes aligned pivot openings through which a pivot pin is positioned to pivotally secure an equipment carrier support member between the upstanding members. The upstanding members also each include two sets of auxiliary openings spaced from the pivot openings and from one another. Depending upon the particular configuration of the support member, each pair of aligned auxiliary openings can be utilized to lock the support member in a transport position, or to stop or maintain the support member in a non-use position.