A bicycle rack for a motorcycle, including a first base member having an adjustable mounting assembly for securely mounting the base member to a motorcycle carrier rack positioned over the rear wheel of a motorcycle. The first base member is elongate and is positioned in a generally transverse orientation relative to the longitudinal axis of the motorcycle. At one end of the first base member there is disposed an adjustable platform for supporting or cradling a bicycle frame at or near the bicycle's bottom bracket. A second base member slidably inserts into the first base member and provides an extendable and retractable stem for adjusting the width of the bicycle rack to accommodate frames of varying sizes. The second base member includes a mounting structure for securing bicycle forks at the drop outs. The assembled and mounted rack secures a bicycle in a collapsed configuration in a transverse orientation on the motorcycle while also ensuring a generally balanced weight distribution of the bicycle over the motorcycle.