The temperature dependence of the c-axis optical conductivity sigma(omega) of optimally and overdoped YBa_2Cu_3O_x (x=6.93 and 7) is reported in the far- (FIR) and mid-infrared (MIR) range. Below T_c we observe a transfer of spectral weight from the FIR not only to the condensate at omega = 0, but also to a new peak in the MIR. This peak is naturally explained as a transverse out-of-phase bilayer plasmon by a model for sigma(omega) which takes the layered crystal structure into account. With decreasing doping the plasmon shifts to lower frequencies and can be identified with the surprising and so far not understood FIR feature reported in underdoped bilayer cuprates.