The described actuation device comprises a casing, intended for the attachment to the handlebar of the bicycle, a cable-winding bobbin, angularly mobile in the casing about a main axis of the device, a first driving mechanism, acting on the bobbin to rotate it in a first angular direction, a second driving mechanism, acting on the bobbin to rotate it in a second angular direction opposite the first, as well as indexer assembly for removably holding the bobbin in predetermined angular positions. In accordance with the invention, the indexer assembly comprise first countering member, to counter the rotation of the bobbin in the first direction, and second countering member, distinct from the first countering member, to counter the rotation of the bobbin in the second direction. Asymmetric operation is thus obtained which allows active actuation to be set both for upward gearshifting and for downward gearshifting.