The influence of non-Newtonian fluid behavior and the Eötvös number on conditional and unconditional second-order structure functions of bubbly channel flows has been investigated by conducting a series of direct numerical simulations at a friction Reynolds number of 127.3. Two Eötvös numbers have been considered (Eo = 0.3125 and Eo = 3.75) together with three different power-law indexes representing shear-thinning (n = 0.7), Newtonian (n = 1.0), and shear-thickening (n = 1.3) fluid behavior. The scaling of the second-order structure functions (SFs) can be translated into an inertial range scaling of the turbulent kinetic energy spectrum. However, because of the discontinuous character of the fluid properties in bubbly flows, SFs are more easily accessible than turbulence spectra, which are based on Fourier transform. It has been found that the different parameters (i.e., Eo, n) have an influence on the energy content as well as the peak location of the compensated second-order SFs (i.e., the dimensions of the large scales). However, after appropriate scaling, the curves nearly collapse. To confirm and further explain the above findings, directional length scales have been evaluated and discussed in detail. Finally, the anisotropy of the Reynolds stress tensor and dissipation tensor has been analyzed in terms of the Lumley triangle, showing that bubbly channel flows are less isotropic than their single-phase counterpart, although they are more homogeneous in the channel center. While the dissipation tensor is slightly more isotropic than the Reynolds stress tensor in the bulk region of the channel flow, overall, a very similar behavior is observed.