In this work, we examine the effect of short-range depletion attraction on the rheology of concentrated bimodal suspensions. The depletion interaction is driven by small particle exclusion from the space between big particles with a magnitude depending on the relative concentration of the constituents. We have chosen two particle size ratios, =3.4 and 6.8, in constant volume fraction phi=0.59 to study the depletion-induced bonding between large particles in the poly(ethylene glycol)/nanosilica suspensions without liquid-liquid phase separation. The clustering of large particles in the samples is characterized via the thixotropic behavior and shear thickening response. Bimodal suspensions with R=0.6 and 0.75 at =6.8 show thixotropy and reduced zero-shear viscosity compared to bimodal samples with the same R at =3.4 size ratio. Additionally, the onset of shear thickening obtained from the experimental and both modeling results occurs at significantly lower shear rates in samples, which contain more clusters of large particles. Finally, we propose a modified state diagram for bimodal concentrated suspensions based on the rheological measurements.