Ferromagnetic/antiferromagnetic bilayers are interfaced with normal metal/ferromagnetic bilayers to form F*/AF/N/F valves. The N-spacer thickness is chosen such that it mediates strong indirect exchange [Ruderman-Kittel-Kasuya-Yosida (RKKY)] between the outer ferromagnetic layers, which varies in strength/direction depending on the N thickness and changes its direction on switching F. The system exhibits a strong modulation of the F*/AF exchange bias, oscillating in strength synchronously with the oscillation in the interlayer RKKY exchange across the normal metal spacer. The effect is explained as due to a superposition taking place within the antiferromagnetic layer of the direct-exchange proximity effect from the F*/AF interface and the indirect RKKY exchange from F penetrating AF via N. The modulation, expressed via the strength of the F*/AF bias field, reaches 400% at the first RKKY peak.