A bumper assembly for use on a cycle steering column, comprising in combination a C-shaped gripper sleeve, an elastomeric bumper attached to the sleeve, and having a bumper surface presented outwardly relative to the sleeve, there being adjustable retainer means configured to releasably hold the bumper and sleeve in selected positions, whereby the sleeve is adjustable endwise and rotatably to adjustably position and retain the sleeve to the steering column, with the bumper presented outwardly, in a selected direction, as aforesaid.