A single-piece side wheel attachment member for removably attaching an auxiliary side wheel to a bicycle is provided. The attachment member has a single-piece molded structure, including an upper vertical portion and a lower substantially horizontal spindle portion connected through a C-shaped compliant structure for allowing the spindle portion to move vertically when subjected to force. In its natural unbiased condition, the vertical and horizontal portions of the member extend generally perpendicular to one another. The upper vertical portion includes a projection and at least one through-hole for insertion on the rear wheel axle of the bicycle. The horizontal spindle portion is rotatably engaged by the auxiliary side wheel, therefore acting as its axle. Both ends of the attachment member can angularly move relative to one another due to the C-shaped compliant structure.