A bicycle suspension assembly elastically supports a first frame member to a second frame member. The suspension assembly preferably forms a bottom bracket unit that allows the rear frame member to pivot about the axis of the bicycle crank axle without any adverse affects to the drive train assembly. Preferably, the suspension assembly includes a first suspension member, a second suspension member, a first bearing unit, and a shock-absorbing structure. The first bearing unit is operatively disposed between the first and second suspension members to movably support the first suspension member for rotation relative to the second suspension member about a center pivot axis. In the preferred embodiment, each of the shock-absorbing structure includes a plurality of biasing members. Preferably, the suspension assembly includes a second bearing unit that is axially spaced from the first bearing unit along the center pivot axis.