A bicycle rim assembly includes a rim defining a central plane and comprising annular inner and outer walls. The outer wall includes first and second bead seats separated by a center well. First and second annular projections are spaced laterally from each other relative to the central plane and extend substantially radially outwardly from the outer wall. Each of the annular projections includes a radially outer face and a laterally inner face. Right and left covers are spaced from each other and are preferably coupled to the rim to cover at least a portion of the laterally inner face and the radially outer face of the first and second annular projections, respectively, and also the first and second bead seats, respectively. One or both of the right and left covers can be fiber reinforced. First and second pieces of tape can be overlapped and used to secure the covers to the rim.